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Annals of Global Analysis and Geometry

, Volume 36, Issue 3, pp 275–284 | Cite as

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

  • J. H. ParkEmail author
  • K. Sekigawa
Original Paper

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 \({\frac{n-2}{r^2}}\).

Keywords

Tangent sphere bundle Contact metric structure η-Einstein manifold 

Mathematics Subject Classification (2000)

Primary 53C25 Secondary 53D10 

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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  1. 1.Department of MathematicsSungkyunkwan UniversitySuwonKorea
  2. 2.Department of MathematicsNiigata UniversityNiigataJapan

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