منابع مشابه
Harmonic 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 کاملHarmonic Morphisms between Semi-riemannian Manifolds
A smooth map f: M ! N between semi-riemannian manifolds is called a harmonic morphism if f pulls back harmonic functions (i.e., local solutions of the Laplace{Beltrami equation) on N into harmonic functions on M. It is shown that a harmonic morphism is the same as a harmonic map which is moreover horizontally weakly conformal, these two notions being likewise carried over from the riemannian ca...
متن کاملHarmonic morphisms of warped product type from Einstein manifolds
Weitzenböck type identities for harmonic morphisms of warped product type are developed which lead to some necessary conditions for their existence. These necessary conditions are further studied to obtain many nonexistence results for harmonic morphisms of warped product type from Einstein manifolds. Mathematics Subject Classification (2000). 58E20, 53C20, 53C25.
متن کاملHarmonic Morphisms with One-dimensional Fibres on Einstein Manifolds
We prove that, from an Einstein manifold of dimension greater than or equal to five, there are just two types of harmonic morphism with one-dimensional fibres. This generalizes a result of R.L. Bryant who obtained the same conclusion under the assumption that the domain has constant curvature.
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.
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ژورنال
عنوان ژورنال: Journal of Geometry and Physics
سال: 2011
ISSN: 0393-0440
DOI: 10.1016/j.geomphys.2010.09.007