Journal of the
Korean Mathematical Society JKMS

We show that the Riemannian geometry of a tangent sphere bundle of a Riemannian manifold $(M,g)$ of constant radius $r$ reduces essentially to the one of unit tangent sphere bundle of a Riemannian manifold equipped with the respective induced Sasaki metrics. Further, we provide some applications of this theorem on the $\eta$-Einstein tangent sphere bundles and certain related topics to the tangent sphere bundles.

Keywords: tangent sphere bundle, contact metric structure, Sasaki metric, $\eta$-Einstein manifold

MSC numbers: 53C25, 53D10, 53B20