### Harmonic morphisms and subharmonic functions.

Choi, Gundon, Yun, Gabjin (2005)

International Journal of Mathematics and Mathematical Sciences

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Choi, Gundon, Yun, Gabjin (2005)

International Journal of Mathematics and Mathematical Sciences

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Atsushi Tachikawa (1992)

Manuscripta mathematica

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Fida El Chami, Georges Habib, Roger Nakad (2015)

Archivum Mathematicum

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In this paper, we consider a Riemannian foliation that admits a nontrivial parallel or harmonic basic form. We estimate the norm of the O’Neill tensor in terms of the curvature data of the whole manifold. Some examples are then given.

Sami Baraket, Dong Ye (1992)

Manuscripta mathematica

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Jerzy J. Konderak (1992)

Publicacions Matemàtiques

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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 and on a tangent bundle (cf. [YI]) and harmonic vector fields generated by them.

Bent Fuglede (1978)

Annales de l'institut Fourier

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A harmonic morphism $f:M\to N$ between Riemannian manifolds $M$ and $N$ is by definition a continuous mappings which pulls back harmonic functions. It is assumed that dim$M\ge $ dim$N$, since otherwise every harmonic morphism is constant. It is shown that a harmonic morphism is the same as a harmonic mapping in the sense of Eells and Sampson with the further property of being semiconformal, that is, a conformal submersion of the points where $df$ vanishes. Every non-constant harmonic morphism is shown to be...

Masanori Kôzaki, Hidekichi Sumi (1989)

Commentationes Mathematicae Universitatis Carolinae

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Todjihounde, Leonard (2006)

International Journal of Mathematics and Mathematical Sciences

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