Comptes Rendus
no. 3-4
Geometry
Killing vector fields of horizontal Liouville type
[Champs de vecteurs de Killing de type de Liouville horizontal]

Présenté par : the Editorial Board

Esmaeil Peyghan1 ; Akbar Tayebi2
1 Department of Mathematics, Faculty of Science, University of Arak, Arak, Iran
2 Department of Mathematics, Faculty of Science, Qom University, Qom, Iran
Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 205-208.

Sur un fibré tangent doté d'une métrique Riemannienne de type Sasaki–Finsler, nous introduisons deux champs de vecteurs de type de Liouville horizontal et nous prouvons que ces champs sont de Killing si et seulement si la variété de Finsler de base possède une courbure constante positive. Dans le cas particulier de l'un d'entre eux, nous montrons que si le champ de vecteurs est de Killing, alors la base est une variété de Finsler–Einstein.

On a slit tangent bundle endowed with a Riemannian metric of Sasaki–Finsler type, we introduce two vector fields of horizontal Liouville type and prove that these vector fields are Killing if and only if the base Finsler manifold is of positive constant curvature. In the special case of one of them, we show that if it is Killing vector field then the base manifold is Einstein–Finsler manifold.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2011.01.009
Esmaeil Peyghan 1 ; Akbar Tayebi 2

1 Department of Mathematics, Faculty of Science, University of Arak, Arak, Iran
2 Department of Mathematics, Faculty of Science, Qom University, Qom, Iran 
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Esmaeil Peyghan; Akbar Tayebi. Killing vector fields of horizontal Liouville type. Comptes Rendus. Mathématique, Volume 349 (2011) no. 3-4, pp. 205-208. doi : 10.1016/j.crma.2011.01.009. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.01.009/

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