NOTES ON TANGENT SPHERE BUNDLES OF CONSTANT RADII

Title & Authors
NOTES ON TANGENT SPHERE BUNDLES OF CONSTANT RADII
Park, Jeong-Hyeong; Sekigawa, Kouei;

Abstract
We show that the Riemannian geometry of a tangent sphere bundle of a Riemannian manifold (M, g) of constant radius $\small{\gamma}$ 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 $\small{\eta}$-Einstein tangent sphere bundles and certain related topics to the tangent sphere bundles.
Keywords
tangent sphere bundle;contact metric structure;Sasaki metric;$\small{\eta}$-Einstein manifold;
Language
English
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