A new quantity in Finsler geometry

Najafi, Behzad; Tayebi, Akbar

doi:10.1016/j.crma.2010.11.015

Differential Geometry

A new quantity in Finsler geometry
[Une nouvelle quantité en géométrie finslerienne]

Présenté par : Jean-Pierre Demailly

Najafi, Behzad ¹ ; Tayebi, Akbar ²

¹ Faculty of Science, Department of Mathematics, Shahed University, Tehran, Iran
² Faculty of Science, Department of Mathematics, Qom University, Qom, Iran

Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 81-83.

Résumé
Abstract

Dans cette Note, nous définissons une nouvelle quantité que nous appelons courbure C-projective de Weyl. Nous montrons que pour une variété de Finsler de dimension $n ⩾ 3$ ayant une courbure de drapeaux de type scalaire, on a $H = 0$ si et seulement si $\tilde{W} = 0$ .

In this Note, we define a new quantity and call it C-projective Weyl curvature. We prove that for a Finsler manifold of scalar flag curvature with dimension $n ⩾ 3$ , $H = 0$ if and only if $\tilde{W} = 0$ .

Reçu le : 2010-06-24
Accepté le : 2010-11-16
Publié le : 2010-11-26

DOI : 10.1016/j.crma.2010.11.015

Affiliations des auteurs :

Najafi, Behzad ¹ ; Tayebi, Akbar ²

¹ Faculty of Science, Department of Mathematics, Shahed University, Tehran, Iran
² Faculty of Science, Department of Mathematics, Qom University, Qom, Iran

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Najafi, Behzad; Tayebi, Akbar. A new quantity in Finsler geometry. Comptes Rendus. Mathématique, Tome 349 (2011) no. 1-2, pp. 81-83. doi : 10.1016/j.crma.2010.11.015. http://archive.numdam.org/articles/10.1016/j.crma.2010.11.015/

Bibliographie
Cité par

[1] Akbar-Zadeh, H. Sur les espaces de Finsler á courbures sectionnelles constantes, Acad. Roy. Belg. Bull. Cl. Sci., Volume 74 (1988), pp. 271-322

[2] Najafi, B.; Shen, Z.; Tayebi, A. Finsler metrics of scalar flag curvature with special non-Riemannian curvature properties, Geom. Dedicata, Volume 131 (2008), pp. 87-97

[3] Mo, X. An Introduction to Finsler Geometry, World Scientific Publishers, 2006

[4] Mo, X. On the non-Riemannian quantity H of a Finsler metric, Diff. Geom. Appl., Volume 27 (2009), pp. 7-14

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