On the geometry of tangent bundles with a class of metrics
Annales Polonici Mathematici, Tome 103 (2012) no. 3, pp. 229-246
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
We introduce a class of metrics on the tangent bundle of a Riemannian manifold and find the Levi-Civita connections of these metrics. Then by using the Levi-Civita connection, we study the conformal vector fields on the tangent bundle of the Riemannian manifold. Finally, we obtain some relations between the flatness (resp. local symmetry) properties of the tangent bundle and the flatness (resp. local symmetry) on the base manifold.
Keywords:
introduce class metrics tangent bundle riemannian manifold levi civita connections these metrics using levi civita connection study conformal vector fields tangent bundle riemannian manifold finally obtain relations between flatness resp local symmetry properties tangent bundle flatness resp local symmetry base manifold
Affiliations des auteurs :
Esmaeil Peyghan 1 ; Abbas Heydari 2 ; Leila Nourmohammadi Far 1
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author = {Esmaeil Peyghan and Abbas Heydari and Leila Nourmohammadi Far},
title = {On the geometry of tangent bundles with a class of metrics},
journal = {Annales Polonici Mathematici},
pages = {229--246},
publisher = {mathdoc},
volume = {103},
number = {3},
year = {2012},
doi = {10.4064/ap103-3-2},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/ap103-3-2/}
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Esmaeil Peyghan; Abbas Heydari; Leila Nourmohammadi Far. On the geometry of tangent bundles with a class of metrics. Annales Polonici Mathematici, Tome 103 (2012) no. 3, pp. 229-246. doi: 10.4064/ap103-3-2
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