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Annals of Global Analysis and Geometry

, Volume 13, Issue 1, pp 91–98 | Cite as

On the curvatures of Einstein spaces

  • Hyoungsick Bahn
  • Sungpyo Hong
Article
  • 94 Downloads

Abstract

For a pseudo-Riemannian manifold (M, g) of dimensionn≥3, we introduce a scalar curvature functionS(V) for non-degenerate subspacesV ofTpM which is a generalization of the scalar curvature, and give some characterizations of Einstein spaces in terms of this scalar curvature function. We also give a characterization for spaces of constant curvature. As an application of our results, we show that the Ricci curvature or the sectional curvature of a Lorentz manifold is constant if the scalar curvature function for non-degenerate subspaces is bounded.

Key words

Scalar curvature Pseudo-Riemannian manifolds Einstein space 

MSC 1991

53B20 53C50 

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References

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Copyright information

© Kluwer Academic Publishers 1995

Authors and Affiliations

  • Hyoungsick Bahn
    • 1
  • Sungpyo Hong
    • 1
  1. 1.Department of MathematicsPohang University of Science and TechnologyPohangKorea

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