On the curvatures of Einstein spaces |
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Authors: | Hyoungsick Bahn Sungpyo Hong |
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Institution: | (1) Department of Mathematics, Pohang University of Science and Technology, 790-784 Pohang, Korea |
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Abstract: | For a pseudo-Riemannian manifold (M, g) of dimensionn 3, we introduce a scalar curvature functionS(V) for non-degenerate subspacesV ofT
pM 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.Partially supported by the grants from TGRC. |
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Keywords: | Scalar curvature Pseudo-Riemannian manifolds Einstein space |
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