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Keywords:
$f$-harmonic morphisms; $f$-harmonic maps; horizontally weakly conformal map
$f$-harmonic morphisms; $f$-harmonic maps; horizontally weakly conformal map
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]).
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