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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-3-2,
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},
volume = {105},
year = {2012},
pages = {229-246},
zbl = {1239.53051},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-3-2}
}
Esmaeil Peyghan; Abbas Heydari; Leila Nourmohammadi Far. On the geometry of tangent bundles with a class of metrics. Annales Polonici Mathematici, Tome 105 (2012) pp. 229-246. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap103-3-2/