Abstract
We show that the Riemannian geometry of a tangent sphere bundle of a Riemannian manifold (M, g) of constant radius <TEX>$\gamma$</TEX> 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 <TEX>$\eta$</TEX>-Einstein tangent sphere bundles and certain related topics to the tangent sphere bundles.
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