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105
Harmonic morphisms and the Jacobi operator
 Rend. Sem. Fac. Sci. Univ. Cagliari
, 2000
"... Abstract. We prove that harmonic morphisms preserve the Jacobi operator along harmonic maps. We apply this result to prove infinitesimal and local rigidity (in the sense of Toth) of harmonic morphisms to a sphere. ..."
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Cited by 2 (1 self)
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Abstract. We prove that harmonic morphisms preserve the Jacobi operator along harmonic maps. We apply this result to prove infinitesimal and local rigidity (in the sense of Toth) of harmonic morphisms to a sphere.
On pHarmonic morphisms
 Diff. Geom. and Appl
, 1998
"... . In this paper, we study the characterisation of pharmonic morphisms between Riemannian manifolds, in the spirit of FugledeIshihara. After a result comparing (2)harmonic morphisms and p harmonic morphisms (p 6= 2), we establish that pharmonic morphisms are precisely horizontally weakly confor ..."
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Cited by 5 (0 self)
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. In this paper, we study the characterisation of pharmonic morphisms between Riemannian manifolds, in the spirit of FugledeIshihara. After a result comparing (2)harmonic morphisms and p harmonic morphisms (p 6= 2), we establish that pharmonic morphisms are precisely horizontally weakly
Isometric Actions And Harmonic Morphisms
 Math. Proc. Cambridge Philos. Soc
, 1999
"... We give the necessary and sufficient condition for a Riemannian foliation, of arbitrary dimension, locally generated by Killing fields to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Introduction It is wellknown that a Riemannian foliation ..."
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Cited by 4 (2 self)
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We give the necessary and sufficient condition for a Riemannian foliation, of arbitrary dimension, locally generated by Killing fields to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Introduction It is wellknown that a Riemannian foliation
Harmonic morphisms between Riemannian manifolds
, 2003
"... Abstract. Harmonic morphisms are mappings between Riemannian manifolds which preserve Laplace’s equation. They can be characterized as harmonic maps which enjoy an extra property called horizontal weak conformality or semiconformality. We shall give a brief survey of the theory concentrating on (i) ..."
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Cited by 161 (27 self)
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Abstract. Harmonic morphisms are mappings between Riemannian manifolds which preserve Laplace’s equation. They can be characterized as harmonic maps which enjoy an extra property called horizontal weak conformality or semiconformality. We shall give a brief survey of the theory concentrating on (i
The Geometry of Pseudo Harmonic Morphisms
"... Abstract. We study a class of maps, called Pseudo Horizontally Weakly Conformal (PHWC), which includes horizontally weakly conformal mappings. We give geometrical conditions ensuring the harmonicity of a (PHWC) map, making it a pseudo harmonic morphism, a generalisation of harmonic morphism, for wh ..."
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Cited by 2 (0 self)
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Abstract. We study a class of maps, called Pseudo Horizontally Weakly Conformal (PHWC), which includes horizontally weakly conformal mappings. We give geometrical conditions ensuring the harmonicity of a (PHWC) map, making it a pseudo harmonic morphism, a generalisation of harmonic morphism
Pseudo Harmonic Morphisms
 Int. J. Math
, 1997
"... Abstract. We study a geometrical condition (PHWC) which is weaker than horizontal weak conformality. In particular, we show that harmonic maps satisfying this condition, which will be called pseudo harmonic morphisms, include harmonic morphisms and can be described as pulling back certain germs to c ..."
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Cited by 11 (3 self)
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Abstract. We study a geometrical condition (PHWC) which is weaker than horizontal weak conformality. In particular, we show that harmonic maps satisfying this condition, which will be called pseudo harmonic morphisms, include harmonic morphisms and can be described as pulling back certain germs
Harmonic morphisms and hyperelliptic graphs
 INTERNATIONAL JOURNAL OF URBAN AND REGIONAL RELATIONSHIPS
, 2007
"... We study harmonic morphisms of graphs as a natural discrete analogue of holomorphic maps between Riemann surfaces. We formulate a graphtheoretic analogue of the classical RiemannHurwitz formula, study the functorial maps on Jacobians and harmonic 1forms induced by a harmonic morphism, and present ..."
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Cited by 31 (2 self)
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We study harmonic morphisms of graphs as a natural discrete analogue of holomorphic maps between Riemann surfaces. We formulate a graphtheoretic analogue of the classical RiemannHurwitz formula, study the functorial maps on Jacobians and harmonic 1forms induced by a harmonic morphism
HARMONIC MORPHISMS AND SUBHARMONIC FUNCTIONS
, 2004
"... Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ: M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map. Similarly ..."
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Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ: M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map
HARMONIC MORPHISMS AND SUBHARMONIC FUNCTIONS
, 2004
"... Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ: M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map. Similarl ..."
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Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ: M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map
HARMONIC MORPHISMS AND SUBHARMONIC FUNCTIONS
, 2004
"... Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ: M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map. Similarl ..."
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Let M be a complete Riemannian manifold and N a complete noncompact Riemannian manifold. Let φ: M → N be a surjective harmonic morphism. We prove that if N admits a subharmonic function with finite Dirichlet integral which is not harmonic, and φ has finite energy, then φ is a constant map
Results 1  10
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105