منابع مشابه
Stability of Harmonic Morphisms
We study the stability of harmonic morphisms as a subclass of harmonic maps. As a general result we show that any harmonic morphism to a manifold of dimension at least three is stable with respect to some Riemannian metric on the target. Furthermore we link the index and nullity of the composition of harmonic morphisms with the index and nullity of the composed maps.
متن کاملHarmonic Morphisms between Riemannian Manifolds
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) twistor methods, (ii) harmonic morphisms with one-dimensional fibres; in particular we shall outline the co...
متن کاملIsometric Actions and Harmonic Morphisms
We give the necessary and suucient condition for a Riemannian foliation, of arbitrary dimension, locally generated by Killing elds to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained.
متن کاملConformal Actions and Harmonic Morphisms
We give necessary and suucient conditions for a conformal foliation locally generated by conformal vector elds to produce harmonic morphisms. Natural constructions of harmonic maps and morphisms are thus obtained. Also we obtain reducibility results for harmonic morphisms induced by (innnitesimal) conformal actions on Einstein manifolds.
متن کاملHarmonic morphisms and subharmonic functions
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, if f is a subharmonic function on N which is not harmonic and such that |df | is bounded, and ...
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ژورنال
عنوان ژورنال: MATHEMATICA SCANDINAVICA
سال: 1993
ISSN: 1903-1807,0025-5521
DOI: 10.7146/math.scand.a-12460