Abstract: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., {\it Harmonic morphisms between Riemannian manifolds\/}, Ann. Inst. Fourier (Grenoble) {\bf 28} (1978), 107--144], [Ishihara T., {\it A mapping of Riemannian manifolds which preserves harmonic functions\/}, J. Math. Kyoto Univ. {\bf 19} (1979), no.~2, 215--229]).
Keywords: $f$-harmonic morphisms; $f$-harmonic maps
AMS Subject Classification: 53C43 58E20