Harmonic Morphisms between Semi-riemannian Manifolds
نویسنده
چکیده
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 case. Additional characterizations of harmonic morphisms are given. The case where M and N have the same dimension n is studied in detail. When n = 2 and the metrics on M and N are indeenite, the harmonic morphisms are characterized essentially by preserving characteristics.
منابع مشابه
Harmonic Morphisms from the Classical Compact Semisimple Lie Groups (version 1.050)
In this paper we introduce a new method for manufacturing complex valued harmonic morphisms from semi-Riemannian manifolds. This is employed to yield a variety of new examples from the compact Riemannian Lie groups SO(n), SU(n), Sp(n). We then develop a duality principle and show how this can be used to construct the first known examples of harmonic mor-phisms from the non-compact semi-Riemanni...
متن کاملHarmonic Morphisms with One-dimensional Fibres on Conformally-flat Riemannian Manifolds
We classify the harmonic morphisms with one-dimensional fibres (1) from real-analytic conformally-flat Riemannian manifolds of dimension at least four, and (2) between conformally-flat Riemannian manifolds of dimensions at least three.
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 کاملHarmonic Morphisms with 1-dim Fibres on 4-dim Einstein Manifolds
Harmonic morphisms are smooth maps between Riemannian manifolds which preserve Laplace's equation. They are characterised as harmonic maps which are horizontally weakly conformal 14, 20]. R.L. Bryant 7] proved that there are precisely two types of harmonic morphisms with one-dimensional bres which can be deened on a constant curvature space of dimension at least four. Here we prove that, on an ...
متن کاملThe Geometry of Harmonic Maps and Morphisms
We give a survey of harmonic morphisms between Riemannian manifolds, concentrating on their construction and relations with the geometry of foliations.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1996