Invariance of g-natural metrics on tangent bundles

Abstract

In this paper we prove that each g-natural metric on a tangent bundle TM over a Riemannian manifold (M, g) is invariant with respect to the induced map of a (local) isometry of the base manifold. Then we apply this result to natural metrics on unit tangent sphere bundles.

Keywords

• Invariance
• g-natural
• metrics
• tangent
• bundles