[Champs de vecteurs de Killing de type de Liouville horizontal]
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.
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@article{CRMATH_2011__349_3-4_205_0,
author = {Peyghan, Esmaeil and Tayebi, Akbar},
title = {Killing vector fields of horizontal {Liouville} type},
journal = {Comptes Rendus. Math\'ematique},
pages = {205--208},
publisher = {Elsevier},
volume = {349},
number = {3-4},
year = {2011},
doi = {10.1016/j.crma.2011.01.009},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.01.009/}
}
TY - JOUR AU - Peyghan, Esmaeil AU - Tayebi, Akbar TI - Killing vector fields of horizontal Liouville type JO - Comptes Rendus. Mathématique PY - 2011 SP - 205 EP - 208 VL - 349 IS - 3-4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.01.009/ DO - 10.1016/j.crma.2011.01.009 LA - en ID - CRMATH_2011__349_3-4_205_0 ER -
%0 Journal Article %A Peyghan, Esmaeil %A Tayebi, Akbar %T Killing vector fields of horizontal Liouville type %J Comptes Rendus. Mathématique %D 2011 %P 205-208 %V 349 %N 3-4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.01.009/ %R 10.1016/j.crma.2011.01.009 %G en %F CRMATH_2011__349_3-4_205_0
Peyghan, Esmaeil; Tayebi, Akbar. Killing vector fields of horizontal Liouville type. Comptes Rendus. Mathématique, Tome 349 (2011) no. 3-4, pp. 205-208. doi : 10.1016/j.crma.2011.01.009. http://www.numdam.org/articles/10.1016/j.crma.2011.01.009/
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