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When are the tangent sphere bundles of a Riemannian manifold η-Einstein?

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Abstract

We study the geometry of a tangent sphere bundle of a Riemannian manifold (M, g). Let M be an n-dimensional Riemannian manifold and T r M be the tangent bundle of M of constant radius r. The main theorem is that T r M equipped with the standard contact metric structure is η-Einstein if and only if M is a space of constant sectional curvature \({\frac{1}{r^2}}\) or \({\frac{n-2}{r^2}}\).

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Authors and Affiliations

  1. Department of Mathematics, Sungkyunkwan University, Suwon, 440-746, Korea

    J. H. Park

  2. Department of Mathematics, Niigata University, Niigata, 950-2181, Japan

    K. Sekigawa

Authors
  1. J. H. Park
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  2. K. Sekigawa
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Corresponding author

Correspondence to J. H. Park.

Additional information

Communicated by: O. Kowalski (Prague).

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Park, J.H., Sekigawa, K. When are the tangent sphere bundles of a Riemannian manifold η-Einstein?. Ann Glob Anal Geom 36, 275–284 (2009). https://doi.org/10.1007/s10455-009-9160-1

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  • DOI: https://doi.org/10.1007/s10455-009-9160-1

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