Comptes Rendus
no. 1-2
Differential Geometry
A new quantity in Finsler geometry
[Une nouvelle quantité en géométrie finslerienne]

Présenté par : Jean-Pierre Demailly

Behzad Najafi1  ; Akbar Tayebi2
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, Volume 349 (2011) no. 1-2, pp. 81-83.

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 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 W˜=0.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2010.11.015
Behzad Najafi 1 ; Akbar Tayebi 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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Behzad Najafi; Akbar Tayebi. A new quantity in Finsler geometry. Comptes Rendus. Mathématique, Volume 349 (2011) no. 1-2, pp. 81-83. doi : 10.1016/j.crma.2010.11.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.11.015/

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

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

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

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

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