Harmonic vector fields on Landsberg manifolds

Alireza Shahi; Behroz Bidabad

doi:10.1016/j.crma.2014.08.002

Differential geometry

Harmonic vector fields on Landsberg manifolds
[Champs de vecteurs harmoniques sur les variétés landsbergiennes]

Présenté par : the Editorial Board

Alireza Shahi ¹ ; Behroz Bidabad ¹

¹ Faculty of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, 15914 Tehran, Iran

Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 737-741.

Résumé
Abstract

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 : 2014-02-12
Accepté le : 2014-08-04
Publié le : 2014-08-27

DOI : 10.1016/j.crma.2014.08.002

Affiliations des auteurs :

Alireza Shahi ¹ ; Behroz Bidabad ¹

¹ Faculty of Mathematics, Amirkabir University of Technology (Tehran Polytechnic), 424 Hafez Avenue, 15914 Tehran, Iran

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     title = {Harmonic vector fields on {Landsberg} manifolds},
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     language = {en},
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Alireza Shahi; Behroz Bidabad. Harmonic vector fields on Landsberg manifolds. Comptes Rendus. Mathématique, Volume 352 (2014) no. 9, pp. 737-741. doi : 10.1016/j.crma.2014.08.002. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2014.08.002/

Bibliographie
Cité par

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Behroz Bidabad; Mir Ahmad Mirshafeazadeh Harmonic vector fields and the Hodge Laplacian operator on Finsler geometry, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 360 (2022), pp. 1193-1204 | DOI:10.5802/crmath.287 | Zbl:1503.58005
Neda Shojaee; Morteza Mirmohammad Rezaii Harmonic vector fields on a weighted Riemannian manifold arising from a Finsler structure, Advances in Pure and Applied Mathematics, Volume 9 (2018) no. 2, pp. 131-141 | DOI:10.1515/apam-2016-0099 | Zbl:1390.58005
Alireza Shahi; Behroz Bidabad Harmonic vector fields on Finsler manifolds, Comptes Rendus. Mathématique. Académie des Sciences, Paris, Volume 354 (2016) no. 1, pp. 101-106 | DOI:10.1016/j.crma.2015.10.006 | Zbl:1350.53097

Cité par 3 documents. Sources : zbMATH

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