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http://dx.doi.org/10.4134/JKMS.2009.46.6.1255

NOTES ON TANGENT SPHERE BUNDLES OF CONSTANT RADII  

Park, Jeong-Hyeong (DEPARTMENT OF MATHEMATICS SUNGKYUNKWAN UNIVERSITY)
Sekigawa, Kouei (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE NIIGATA UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.46, no.6, 2009 , pp. 1255-1265 More about this Journal
Abstract
We show that the Riemannian geometry of a tangent sphere bundle of a Riemannian manifold (M, g) of constant radius $\gamma$ 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 $\eta$-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;
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