Conformally flat tangent bundles with general natural lifted metrics

Abstract

We study the conditions under which the tangent bundle $(TM,G)$ of an $n$-dimensional Riemannian manifold $(M,g)$ is conformally flat, where $G$ is a general natural lifted metric of $g$. We prove that the base manifold must have constant sectional curvature and we find some expressions for the natural lifted metric $G$, such that the tangent bundle $(TM,G)$ become conformally flat.

12 pages, contribution to The Eight International Workshop on Differential Geomerty and Its Applications, August 19 25, 2007, "Babes Bolyai" University, Cluj Napoca, Romania

References in corpus (1)

• Cheeger Gromoll type metrics on the tangent bundle