[Sur une classe de métriques riemanniennes issues de structures finsleriennes]
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.
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@article{CRMATH_2011__349_5-6_319_0,
author = {Tayebi, Akbar and Peyghan, Esmaeil},
title = {On a class of {Riemannian} metrics arising from {Finsler} structures},
journal = {Comptes Rendus. Math\'ematique},
pages = {319--322},
publisher = {Elsevier},
volume = {349},
number = {5-6},
year = {2011},
doi = {10.1016/j.crma.2011.01.021},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.01.021/}
}
TY - JOUR AU - Tayebi, Akbar AU - Peyghan, Esmaeil TI - On a class of Riemannian metrics arising from Finsler structures JO - Comptes Rendus. Mathématique PY - 2011 SP - 319 EP - 322 VL - 349 IS - 5-6 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.01.021/ DO - 10.1016/j.crma.2011.01.021 LA - en ID - CRMATH_2011__349_5-6_319_0 ER -
%0 Journal Article %A Tayebi, Akbar %A Peyghan, Esmaeil %T On a class of Riemannian metrics arising from Finsler structures %J Comptes Rendus. Mathématique %D 2011 %P 319-322 %V 349 %N 5-6 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.01.021/ %R 10.1016/j.crma.2011.01.021 %G en %F CRMATH_2011__349_5-6_319_0
Tayebi, Akbar; Peyghan, Esmaeil. On a class of Riemannian metrics arising from Finsler structures. Comptes Rendus. Mathématique, Tome 349 (2011) no. 5-6, pp. 319-322. doi : 10.1016/j.crma.2011.01.021. http://www.numdam.org/articles/10.1016/j.crma.2011.01.021/
[1] On Einstein Riemannian g-natural metrics on unit tangent sphere bundles, Ann. Global Anal. Geom., Volume 38 (2010) no. 1, pp. 11-20
[2] Finsler Geometry and Applications, Ellis Horwood, New York, 1990
[3] A geometric characterization of Finsler manifolds of constant curvature , Internat. J. Math. Math. Sci., Volume 23 (2000), pp. 399-407
[4] Finsler metrics of positive constant flag curvature on Sasakian space forms, Hokkaido Math. J., Volume 31 (2002), pp. 459-468
[5] Foliation and Geometrics Structures, Springer, 2006
[6] Finsler geometry and natural foliations on the tangent bundle, Rep. Math. Phys., Volume 58 (2006), pp. 131-146
[7] On totally geodesic foliations with bundle-like metric, J. Geom., Volume 85 (2006), pp. 7-14
[8] A Kähler structure on the non-zero tangent bundle of a space form, Diff. Geom. Appl., Volume 11 (1999), pp. 1-12
[9] Cohomology and Differential Forms, Marcel Dekker Inc., New York, 1973
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