Conformally flat tangent bundles with general natural lifted metrics

Mathematics – Differential Geometry

Scientific paper

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12 pages, contribution to The Eight International Workshop on Differential Geomerty and Its Applications, August 19 25, 2007,

Scientific paper

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.

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