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Rigidity of noncompact complete manifolds with harmonic curvature

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Let (M, g) be a noncompact complete n-manifold with harmonic curvature and positive Sobolev constant. Assume that the L 2 norms of the traceless Ricci curvature are finite. We prove that (M, g) is Einstein if n ≥ 5 and the L n/2 norms of the Weyl curvature and traceless Ricci curvature are small enough.

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  1. Department of Mathematics Education, Inha University, Incheon, 402-751, Korea

    Seongtag Kim

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  1. Seongtag Kim
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Correspondence to Seongtag Kim.

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Kim, S. Rigidity of noncompact complete manifolds with harmonic curvature. manuscripta math. 135, 107–116 (2011). https://doi.org/10.1007/s00229-010-0412-y

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  • DOI: https://doi.org/10.1007/s00229-010-0412-y

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