Harmonic morphisms between riemannian manifolds
- 1 January 1978
- journal article
- Published by Cellule MathDoc/Centre Mersenne in Annales de l'institut Fourier
- Vol. 28 (2) , 107-144
- https://doi.org/10.5802/aif.691
Abstract
Summary:In this paper, we study the characterization of generalized $f$-harmonic morphisms between Riemannian manifolds. We prove that a map between Riemannian manifolds is an $f$-harmonic morphism if and only if it is a horizontally weakly conformal map satisfying some further conditions. We present new properties generalizing Fuglede-Ishihara characterization for harmonic morphisms ([Fuglede B., Harmonic morphisms between Riemannian manifolds, Ann. Inst. Fourier (Grenoble) 28 (1978), 107--144], [Ishihara T., A mapping of Riemannian manifolds which preserves harmonic functions, J. Math. Kyoto Univ. 19 (1979), no. 2, 215--229])Keywords
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