On the geometry of tangent bundles with a class of metrics
Volume 103 / 2012
Annales Polonici Mathematici 103 (2012), 229-246
MSC: Primary 53C20; Secondary 53C22.
DOI: 10.4064/ap103-3-2
Abstract
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.
