On a class of Riemannian metrics arising from Finsler structures

Akbar Tayebi; Esmaeil Peyghan

doi:10.1016/j.crma.2011.01.021

Geometry

On a class of Riemannian metrics arising from Finsler structures
[Sur une classe de métriques riemanniennes issues de structures finsleriennes]

Présenté par : Jean-Pierre Demailly

Akbar Tayebi ¹ ; Esmaeil Peyghan ²

¹ Department of Mathematics, Faculty of Science, Qom University, Qom, Iran
² Department of Mathematics, Faculty of Science, University of Arak, Arak, Iran

Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 319-322.

Résumé
Abstract

Sur le fibré tangent dʼune variéte finslerienne, nous introduisons une certaines classe de métriques et étudions la relation entre la connexion de Levi-Civita, la connexion de Vaisman, et les espaces de Reinhart. Nous montrons que les connexions de Levi-Civita et de Vaisman induisent les mêmes connexions dans le fibré structurel si seulement si la variété de base est de Landsberg. En outre, toute varété de Reinhart feuilletée se réduit à une variété riemannienne.

On the slit tangent bundle of Finsler manifolds, we introduce a class of metrics and study the relation between Levi-Civita connection, Vaisman connection, vertical foliation, and Reinhart spaces. We show that the Levi-Civita and the Vaisman connections induce the same connections in the structural bundle if and only if the base manifold is Landsbergian. Moreover every foliated Reinhart manifold reduces to a Riemannian manifold.

Reçu le : 2010-12-20
Accepté le : 2011-01-21
Publié le : 2011-02-18

DOI : 10.1016/j.crma.2011.01.021

Affiliations des auteurs :

Akbar Tayebi ¹ ; Esmaeil Peyghan ²

¹ Department of Mathematics, Faculty of Science, Qom University, Qom, Iran
² Department of Mathematics, Faculty of Science, University of Arak, Arak, Iran

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     title = {On a class of {Riemannian} metrics arising from {Finsler} structures},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {319--322},
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     year = {2011},
     doi = {10.1016/j.crma.2011.01.021},
     language = {en},
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Akbar Tayebi; Esmaeil Peyghan. On a class of Riemannian metrics arising from Finsler structures. Comptes Rendus. Mathématique, Volume 349 (2011) no. 5-6, pp. 319-322. doi : 10.1016/j.crma.2011.01.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.01.021/

Bibliographie
Cité par

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