no. 9
Differential geometry
Harmonic vector fields on Landsberg manifolds
[Champs de vecteurs harmoniques sur les variétés landsbergiennes]

Présenté par : the Editorial Board

Shahi, Alireza1 ; Bidabad, Behroz1 
1 Faculty of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, 15914 Tehran, Iran
Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 737-741.

Soit (M,F) une variété landsbergienne compacte sans bord. Dans cet article, il est obtenu une condition nécessaire et suffisante pour qu'un champ de vecteurs sur (M,F) soit harmonique. On donne ensuite un énoncé analogue sur une variété finslérienne compacte sans bord. En outre, on étudie la non-existence de champs de vecteurs harmoniques sur les variétés landsbergiennes compactes et, enfin, une borne supérieure pour le premier groupe de cohomologie de de Rham est obtenue.

Let (M,F) be a compact boundaryless Landsberg manifold. In this work, a necessary and sufficient condition for a vector field on (M,F) to be harmonic is obtained. Next, on a compact boundaryless Finsler manifold of zero flag curvature, a necessary and sufficient condition for a vector field to be harmonic is found. Furthermore, the nonexistence of harmonic vector fields on a compact Landsberg manifold is studied and an upper bound for the first de Rham cohomology group is obtained.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2014.08.002
Shahi, Alireza 1 ; Bidabad, Behroz 1

1 Faculty of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, 15914 Tehran, Iran 
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Shahi, Alireza; Bidabad, Behroz. Harmonic vector fields on Landsberg manifolds. Comptes Rendus. Mathématique, Tome 352 (2014) no. 9, pp. 737-741. doi : 10.1016/j.crma.2014.08.002. http://www.numdam.org/articles/10.1016/j.crma.2014.08.002/

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