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Sökning: WFRF:(Gudmundsson Sigmundur)

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1.
  • Andersdotter Svensson, Emma, et al. (författare)
  • Natural almost Hermitian structures on conformally foliated 4-dimensional Lie groups with minimal leaves
  • 2023
  • Ingår i: Rendiconti del Circolo Matematico di Palermo. - : Springer Science and Business Media LLC. - 0009-725X .- 1973-4409. ; 72, s. 2265-2286
  • Tidskriftsartikel (refereegranskat)abstract
    • Let (G, g) be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation F with minimal leaves. Let J be an almost Hermitian structure on G adapted to the foliation F . We classify such structures J which are almost Kähler (AK), integrable (I) or Kähler (K). Hereby we construct several new multi-dimensional examples in each class.
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3.
  • Burel, J-M, et al. (författare)
  • On the geometry of the Gauss map of conformal foliations by lines
  • 2004
  • Ingår i: Mathematical Proceedings of the Cambridge Philosophical Society. - 1469-8064. ; 136, s. 247-255
  • Tidskriftsartikel (refereegranskat)abstract
    • Let F be an oriented conformal foliation of connected, totally geodesic and 1-dimensional leaves in Rn+1. We prove that if n greater than or equal to 3 then the Gauss map phi: U --> S-n of F is a non-constant n-harmonic morphism if and only if it is a radial projection.
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4.
  • Ghandour, Elsa, et al. (författare)
  • Explicit p-harmonic functions on the real Grassmannians
  • 2023
  • Ingår i: Advances in Geometry. - 1615-7168.
  • Tidskriftsartikel (refereegranskat)abstract
    • In this work we use the method of eigenfamilies to construct explicit complex-valued proper p-harmonic functions on the compact real Grassmannians. We also find proper p-harmonic functions on the real flag manifolds which do not descend onto any of the real Grassmannians
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5.
  • Ghandour, Elsa, et al. (författare)
  • Proper biharmonic maps and (2,1) -harmonic morphisms from some wild geometries
  • 2023
  • Ingår i: Rendiconti del Circolo Matematico di Palermo. - 0009-725X. ; 72:8, s. 4101-4114
  • Tidskriftsartikel (refereegranskat)abstract
    • In this work we construct a variety of new complex-valued proper biharmonic maps and (2, 1)-harmonic morphisms on Riemannian manifolds with non-trivial geometry. These are solutions to a non-linear system of partial differential equations depending on the geometric data of the manifolds involved.
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6.
  • Gudmundsson, Sigmundur (författare)
  • A note on biharmonic functions on the Thurston geometries
  • 2018
  • Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 131, s. 114-121
  • Tidskriftsartikel (refereegranskat)abstract
    • We construct new explicit proper biharmonic functions on the 3-dimensional Thurston geometries Sol, Nil, SL˜2(R), H2×R and S2×R.
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7.
  • Gudmundsson, Sigmundur, et al. (författare)
  • A note on the classification of holomorphic harmonic morphisms
  • 1993
  • Ingår i: Potential Analysis. - 1572-929X. ; 2:3, s. 295-298
  • Tidskriftsartikel (refereegranskat)abstract
    • In this note we give a complete classification of those holomorphic maps phgr:UrarrCopf n defined on open and connected subsets of Copf m which are harmonic morphisms.
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10.
  • Gudmundsson, Sigmundur (författare)
  • Biharmonic functions on spheres and hyperbolic spaces
  • 2018
  • Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 134, s. 244-248
  • Tidskriftsartikel (refereegranskat)abstract
    • We construct new explicit proper r-harmonic functions on the standard n-dimensional hyperbolic spaces H^n and spheres S^n for any r ≥ 1 and n ≥ 2.
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11.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Biharmonic functions on the classical compact simple Lie groups
  • 2018
  • Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1559-002X .- 1050-6926. ; 28:2, s. 1525-1547
  • Tidskriftsartikel (refereegranskat)abstract
    • The main aim of this work is to construct several new families of proper biharmonic functions defined on open subsets of the classical compact simple Lie groups SU(n), SO(n) and Sp(n). We work in a geometric setting which connects our study with the theory of submersive harmonic morphisms. We develop a general duality principle and use this to interpret our new examples on the Euclidean sphere S^3 and on the hyperbolic space H^3.
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12.
  • Gudmundsson, Sigmundur (författare)
  • Biharmonic functions on the special unitary group SU(2)
  • 2017
  • Ingår i: Differential Geometry and its Applications. - : Elsevier BV. - 0926-2245. ; 53, s. 137-147
  • Tidskriftsartikel (refereegranskat)abstract
    • We construct new proper biharmonic functions defined on open and dense subsets of the special unitary group SU(2). Then we employ a duality principle to obtain new proper biharmonic functions from the non-compact 3-dimensional hyperbolic space H^3.
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13.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Complete minimal submanifolds of compact Lie groups
  • 2016
  • Ingår i: Mathematische Zeitschrift. - : Springer Science and Business Media LLC. - 0025-5874 .- 1432-1823. ; 282, s. 993-1005
  • Tidskriftsartikel (refereegranskat)abstract
    • We give a new method for manifacturing complete minimal submanifolds of compact Lie groups and their homogeneous quotient spaces. For this we make use of harmonic morphisms and basic representation theory of Lie groups. We then employ our method to construct many examples of compact minimal submanifolds of the special unitary groups.
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14.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Complex-valued (p,q)-harmonic morphisms from Riemannian manifolds
  • 2021
  • Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1559-002X .- 1050-6926. ; 31:11, s. 11386-11409
  • Tidskriftsartikel (refereegranskat)abstract
    • We introduce the natural notion of (p,q)-harmonic morphisms between Riemannian manifolds. This unifies several theories that have been studied during the last decades. We then study the special case when the maps involved are complex-valued. For these we find a characterisation and provide new non-trivial examples in important cases.
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15.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Conformal foliations on Lie groups and complex-valued harmonic morphisms
  • 2021
  • Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 159
  • Tidskriftsartikel (refereegranskat)abstract
    • We study left-invariant foliations F on Riemannian Lie groups G generated by a subgroup K. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations F when the subgroup K is one of the important SU(2)*SU(2), SU(2)*SL_2(R), SU(2)*SO(2) or SL_2(R)*SO(2). By this we yield new multi-dimensional families of Lie groups G carrying such foliations in each case. These foliations F produce local complex-valued harmonic morphisms on the corresponding Lie group G.
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16.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Conformal minimal foliations on semi-Riemannian Lie groups
  • 2022
  • Ingår i: Journal of Geometry and Symmetry in Physics. - 1312-5192. ; 63, s. 1-20
  • Tidskriftsartikel (refereegranskat)abstract
    • We study left-invariant foliations F on semi-Riemannian Lie groups G generated by a subgroup K. We are interested in such foliations which are conformal and with minimal leaves of codimension two. We classify such foliations F when the subgroup K is one of the important groups SU(2), SL_2(R), SU(2)*SU(2), SU(2)*SL_2(R)$, SU(2)*SO(2), SL_2(R)*SO(2). This way we construct new multi-dimensional families of Lie groups G carrying such foliations in each case. These foliations F produce local complex-valued harmonic morphisms on the corresponding Lie group G.
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17.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Explicit harmonic morphisms and p-harmonic functions from the complex and quaternionic Grassmannians
  • 2023
  • Ingår i: Annals of Global Analysis and Geometry. - 1572-9060. ; 64:2
  • Tidskriftsartikel (refereegranskat)abstract
    • We construct explicit complex-valued p-harmonic functions and harmonic morphisms on the classical compact symmetric complex and quaternionic Grassmannians. The ingredients for our construction method are joint eigenfunctions of the classical Laplace-Beltrami and the so called conformality operator. A known duality principle implies that these p-harmonic functions and harmonic morphisms also induce such solutions on the Riemannian symmetric non-compact dual spaces.
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18.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Explicit p-harmonic functions on rank-one Lie groups of Iwasawa type
  • 2021
  • Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 164
  • Tidskriftsartikel (refereegranskat)abstract
    • We construct explicit proper p-harmonic functions on rank-one Lie groups of Iwasawa type. This class of Lie groups includes many classical Riemannian manifolds such as the rank-one symmetric spaces of non-compact type, Damek-Ricci spaces, rank-one Einstein solvmanifolds and Carnot spaces
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20.
  • Gudmundsson, Sigmundur (författare)
  • Harmonic morphisms as sphere bundles over compact Riemann surfaces
  • 1997
  • Ingår i: International Journal of Mathematics. - 0129-167X. ; 8:7, s. 935-942
  • Tidskriftsartikel (refereegranskat)abstract
    • We prove that the projection map of an orientable sphere bundle, over a compact Riemann surface, of any homotopy type can be realized as a harmonic morphism with totally geodesic fibres.
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24.
  • Gudmundsson, Sigmundur (författare)
  • Harmonic morphisms between spaces of constant curvature
  • 1993
  • Ingår i: Proceedings of the Edinburgh Mathematical Society. - 1464-3839. ; 36, s. 133-143
  • Tidskriftsartikel (refereegranskat)abstract
    • Let M and N be simply connected space forms, and U an open and connected subset of M. Further let n: U-*N be a horizontally homothetic harmonic morphism. In this paper we show that if n has totally geodesic fibres and integrable horizontal distribution, then the horizontal foliation of U is totally umbilic and isoparametric. This leads to a classification of such maps. We also show that horizontally homothetic harmonic morphisms of codimension one are either Riemannian submersions modulo a constant, or up to isometries of M and N one of six well known examples.
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25.
  • Gudmundsson, Sigmundur (författare)
  • Harmonic morphisms from complex projective spaces
  • 1994
  • Ingår i: Geometriae Dedicata. - 0046-5755. ; 53:2, s. 155-161
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we study harmonic morphisms emptyv :U sub CopfP m rarrN 2 from open subsets of complex projective spaces to Riemann surfaces. We construct many new examples of such maps which are not holomorphic with respect to the standard Kähler structure on CopfP m.
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26.
  • Gudmundsson, Sigmundur (författare)
  • Harmonic morphisms from five-dimensional Lie groups
  • 2016
  • Ingår i: Geometriae Dedicata. - : Springer Science and Business Media LLC. - 0046-5755 .- 1572-9168. ; 184:1, s. 143-157
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider 5-dimensional Lie groups equipped with a left-invariant Riemannian metric. On such groups we construct left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce complex-valued harmonic morphisms locally defined on the Lie group.
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27.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Harmonic morphisms from four-dimensional Lie groups
  • 2014
  • Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 83, s. 1-11
  • Tidskriftsartikel (refereegranskat)abstract
    • We consider 4-dimensional Lie groups with left-invariant Riemannian metrics. For such groups we classify left-invariant conformal foliations with minimal leaves of codimension 2. These foliations produce local complex-valued harmonic morphisms.
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28.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Harmonic morphisms from homogeneous Hadamard manifolds
  • 2011
  • Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 1572-9060 .- 0232-704X. ; 39, s. 215-230
  • Tidskriftsartikel (refereegranskat)abstract
    • We present a new method for manufacturing complex-valued harmonic morphisms from a wide class of Riemannian Lie groups. This yields new solutions from an important family of homogeneous Hadamard manifolds. We also give a new method for constructing left-invariant foliations on a large class of Lie groups producing harmonic morphisms.
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29.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Harmonic morphisms from homogeneous spaces of positive curvature
  • 2014
  • Ingår i: Mathematical Proceedings of the Cambridge Philosophical Society. - 1469-8064. ; 157:2, s. 321-327
  • Tidskriftsartikel (refereegranskat)abstract
    • We prove local existence of complex-valued harmonic morphisms from any Riemannian homogeneous spaces of positive curvature, except the Berger space Sp(2)/SU(2)
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30.
  • Gudmundsson, Sigmundur (författare)
  • Harmonic morphisms from quaternionic projective spaces
  • 1995
  • Ingår i: Geometriae Dedicata. - 0046-5755. ; 56:3, s. 327-332
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we give a method for constructing harmonic morphisms from quaternionic projective spaces HopfP k with values in a Riemann surface.
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31.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Harmonic morphisms from solvable Lie groups
  • 2009
  • Ingår i: Mathematical Proceedings of the Cambridge Philosophical Society. - 1469-8064. ; 147:2, s. 389-408
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we introduce two new methods for constructing harmonic morphisms from solvable Lie groups. The first method yields global solutions from any simply connected nilpotent Lie group and from any Riemannian symmetric space of non-compact type and rank r ≥ 3. The second method provides us with global solutions from any Damek–Ricci space and many non-compact Riemannian symmetric spaces. We then give a continuous family of 3-dimensional solvable Lie groups not admitting any complex-valued harmonic morphisms, not even locally.
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32.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Harmonic morphisms from the compact semisimple Lie groups and their non-compact duals
  • 2006
  • Ingår i: Differential Geometry and its Applications. - : Elsevier BV. - 1872-6984 .- 0926-2245. ; 24:4, s. 351-366
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we prove the local existence of complex-valued harmonic morphisms from any compact semisimple Lie group and their non-compact duals. These include all Riemannian symmetric spaces of types II and IV. We produce a variety of concrete harmonic morphisms from the classical compact simple Lie groups SO(n), SU(n), Sp(n) and globally defined solutions on their non-compact duals SO(n, C)/SO(n), SLn (C)/SU(n) and Sp(n, C)/Sp(n). (c) 2005 Elsevier B.V. All rights reserved.
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33.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Harmonic morphisms from the Grassmannians and their non-compact duals
  • 2006
  • Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 1572-9060 .- 0232-704X. ; 30:4, s. 313-333
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we give a unified framework for the construction of complex valued harmonic morphisms from the real, complex and quaternionic Grassmannians and their non-compact duals. This gives a positive answer to the corresponding open existence problem in the real and quaternionic cases.
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34.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Harmonic morphisms on Lie groups and minimal conformal foliations of codimension two
  • 2024
  • Ingår i: Journal of Geometry and Physics. - 0393-0440. ; 198
  • Tidskriftsartikel (refereegranskat)abstract
    • Let G be a Lie group equipped with a left-invariant semi-Riemannian metric. Let K be a semisimple subgroup of G generating a left-invariant conformal foliation F of codimension two on G. We then show that the foliation F is minimal. This means that locally the leaves of F are fibres of a complex-valued harmonic morphism. In the Riemannian case, we prove that if the metric restricted to K is biinvariant then F is totally geodesic.
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35.
  • Gudmundsson, Sigmundur (författare)
  • Holomorphic harmonic morphisms from cosymplectic almost Hermitian manifolds
  • 2015
  • Ingår i: Geometriae Dedicata. - : Springer Science and Business Media LLC. - 0046-5755 .- 1572-9168. ; 178:1, s. 143-150
  • Tidskriftsartikel (refereegranskat)abstract
    • We study 4-dimensional Riemannian manifolds equipped with a minimal and conformal foliation F of codimension 2. We prove that the two adapted almost Hermitian structures J_1 and J_2 are both cosymplectic if and only if F is Riemannian and its horizontal distribution H is integrable.
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36.
  • Gudmundsson, Sigmundur (författare)
  • Holomorphic harmonic morphisms from four-dimensional non-Einstein manifolds
  • 2015
  • Ingår i: International Journal of Mathematics. - 0129-167X. ; 26:1
  • Tidskriftsartikel (refereegranskat)abstract
    • We construct 4-dimensional Riemannian Lie groups carrying left-invariant conformal foliations with minimal leaves of codimension 2. We show that these foliations are holomorphic with respect to an (integrable) Hermitian structure which is not Kähler. We then prove that the Riemannian Lie groups constructed are not Einstein manifolds. This answers an important open question in the theory of complex-valued harmonic morphisms from Riemannian 4-manifolds.
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37.
  • Gudmundsson, Sigmundur (författare)
  • Minimal submanifolds of hyperbolic spaces via harmonic morphisms
  • 1996
  • Ingår i: Geometriae Dedicata. - 0046-5755. ; 62:3, s. 269-279
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we give a method for constructing complete minimal submanifolds of the hyperbolic spaces H-m. They are regular fibres of harmonic morphisms from H-m with values in Riemann surfaces.
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38.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Minimal submanifolds via complex-valued eigenfunctions
  • 2024
  • Ingår i: Journal of Geometric Analysis. - 1559-002X. ; 34:6
  • Tidskriftsartikel (refereegranskat)abstract
    • In this work we introduce a new method for manufacturing minimal submanifolds of Riemannian manifolds of codimension two. For this we employ the so called complex-valued eigenfunctions. This is particularly interesting in the cases when the Riemannian ambient manifold is compact. We then give several explicit examples in important cases.
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39.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Multivalued harmonic morphisms
  • 1993
  • Ingår i: Mathematica Scandinavica. - 0025-5521. ; 73, s. 127-155
  • Tidskriftsartikel (refereegranskat)
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40.
  • Gudmundsson, Sigmundur, et al. (författare)
  • New biharmonic functions on the compact Lie groups SO(n), SU(n), Sp(n)
  • 2021
  • Ingår i: Journal of Geometric Analysis. - : Springer Science and Business Media LLC. - 1559-002X .- 1050-6926. ; 31:1, s. 250-281
  • Tidskriftsartikel (refereegranskat)abstract
    • We develop a new scheme for the construction of explicit complex-valued proper biharmonic functions on Riemannian Lie groups. We exploit this and manufacture many infinite series of uncountable families of new solutions on the special unitary group SU(n). We then show that the special orthogonal group SO(n) and the quaternionic unitary group Sp(n) fall into the scheme. As a by-product we obtain new harmonic morphisms on these groups. All the constructed maps are defined on open and dense subsets of the corresponding spaces.
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41.
  • Gudmundsson, Sigmundur (författare)
  • Non-holomorphic harmonic morphisms from Kähler manifolds
  • 1994
  • Ingår i: Manuscripta Mathematica. - 1432-1785. ; 85:1, s. 67-78
  • Tidskriftsartikel (refereegranskat)abstract
    • We give a method for constructing non-holomorphic harmonic morphisms from Kähler manifolds. The method is then used to obtain many such examples defined locally on the complex Grassmannians.
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42.
  • Gudmundsson, Sigmundur, et al. (författare)
  • On the existence of harmonic morphisms from certain symmetric spaces
  • 2007
  • Ingår i: Journal of Geometry and Physics. - : Elsevier BV. - 0393-0440. ; 57:2, s. 353-366
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we give a positive answer to the open existence problem for complex-valued harmonic morphisms from the non-compact irreducible Riemannian symmetric spaces SLn (R)/SO(n), SU*(2n)/Sp(n) and their compact duals SU(n)/SO(n) and SU(2n)/Sp(n). Furthermore we prove the existence of globally defined, complex-valued harmonic morphisms from any Riemannian symmetric space of type IV.
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43.
  • Gudmundsson, Sigmundur (författare)
  • On the existence of harmonic morphisms from symmetric spaces of rank one
  • 1997
  • Ingår i: Manuscripta Mathematica. - 1432-1785. ; 93:4, s. 421-433
  • Tidskriftsartikel (refereegranskat)abstract
    • In this paper we give a unified framework for constructing harmonic morphisms from the irreducible Riemannian symmetric spaces HHn, CHn, RH2n+l, HPn, CPn and RP2n+1 of rank one. Using this we give a positive answer to the global existence problem for the non-compact hyperbolic cases.
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44.
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46.
  • Gudmundsson, Sigmundur (författare)
  • On the geometry of harmonic morphisms
  • 1990
  • Ingår i: Mathematical Proceedings of the Cambridge Philosophical Society. - 1469-8064. ; 108:3, s. 461-466
  • Tidskriftsartikel (refereegranskat)abstract
    • Let π:M→B be a horizontally conformal submersion. We give necessary curvature conditions on the manifolds M and B, which lead to non-existence results for certain horizontally conformal maps, and harmonic morphisms. We then classify all such maps between open subsets of Euclidean spaces, which additionally have totally geodesic fibres and are horizontally homothetic. They are orthogonal projections on each connected component, followed by a homothety.
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47.
  • Gudmundsson, Sigmundur, et al. (författare)
  • On the geometry of tangent bundles
  • 2002
  • Ingår i: Expositiones Mathematicae. - 0723-0869. ; 20:1, s. 1-41
  • Tidskriftsartikel (refereegranskat)
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48.
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49.
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50.
  • Gudmundsson, Sigmundur, et al. (författare)
  • Proper r-harmonic functions from Riemannian manifolds
  • 2020
  • Ingår i: Annals of Global Analysis and Geometry. - : Springer Science and Business Media LLC. - 0232-704X .- 1572-9060. ; 57, s. 217-223
  • Tidskriftsartikel (refereegranskat)abstract
    • We introduce a new method for constructing complex-valued r-harmonic functions on Riemannian manifolds. We then apply this for the important semisimple Lie groups SO(n) , SU(n) , Sp(n) , SLn(R) , Sp(n, R) , SU(p, q) , SO(p, q) , Sp(p, q) , SO∗(2 n) and SU∗(2 n).
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  • Resultat 1-50 av 55

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