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Comptes Rendus Mathématique
Volume 354, n° 1
pages 101-106 (janvier 2016)
Doi : 10.1016/j.crma.2015.10.006
Received : 15 June 2015 ;  accepted : 2 October 2015
Harmonic vector fields on Finsler manifolds
Champs de vecteurs harmoniques sur les variétés finslériennes
 

Alireza Shahi , Behroz Bidabad
 Faculty of Mathematics and Computer Science, Amirkabir University of Technology (Tehran Polytechnic), Iran 

Abstract

Let   be a compact boundaryless Finsler manifold. In this work, a sufficient condition for a vector field on   to be harmonic is obtained. Next the harmonic vector fields on Finsler manifolds are characterized and an upper bound for the first horizontal de Rham cohomology group of the sphere bundle SM is obtained.

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Résumé

Soit   une variété finslérienne compacte sans bord. Dans cet article, nous donnons une condition suffisante pour qu'un champ de vecteurs sur   soit harmonique. Par ailleurs, nous obtenons une caractérisation des champs de vecteurs harmoniques sur les variétés finslériennes, ainsi qu'une borne supérieure pour le premier groupe horizontal de cohomologie de de Rham du fibré en sphères SM .

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Keywords : Finsler manifolds, Harmonic vector fields, Landsberg




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