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On generalized f -harmonic morphisms

A. Mohammed Cherif, Djaa Mustapha (2014)

Commentationes Mathematicae Universitatis Carolinae

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...

On harmonic vector fields.

Jerzy J. Konderak (1992)

Publicacions Matemàtiques

A tangent bundle to a Riemannian manifold carries various metrics induced by a Riemannian tensor. We consider harmonic vector fields with respect to some of these metrics. We give a simple proof that a vector field on a compact manifold is harmonic with respect to the Sasaki metric on TM if and only if it is parallel. We also consider the metrics II and I + II on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them.

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