Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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NOTES ON TANGENT SPHERE BUNDLES OF CONSTANT RADII

  • Published : 2009.11.01
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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.

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References

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  2. Tangent sphere bundles with constant trace of the Jacobi operator vol.53, pp.2, 2012, https://doi.org/10.1007/s13366-011-0057-3
  3. Spectral geometry of eta-Einstein Sasakian manifolds vol.62, pp.11, 2012, https://doi.org/10.1016/j.geomphys.2012.06.007
  4. When are the tangent sphere bundles of a Riemannian manifold η-Einstein? vol.36, pp.3, 2009, https://doi.org/10.1007/s10455-009-9160-1