Geodesic
On generalized $f$-harmonic morphisms
Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 1, pp. 17-27.

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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]).
Classification : 53C43, 58E20
Keywords: $f$-harmonic morphisms; $f$-harmonic maps; horizontally weakly conformal map 
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Cherif, A. Mohammed; Mustapha, Djaa. On generalized $f$-harmonic morphisms. Commentationes Mathematicae Universitatis Carolinae, Tome 55 (2014) no. 1, pp. 17-27. http://geodesic.mathdoc.fr/item/CMUC_2014__55_1_a2/