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arXiv · 0911.2694

Rigidity of noncompact complete manifolds with harmonic curvature

Seongtag Kim
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Abstract

Let $(M,g)$ be a noncompact complete $n$-manifold with harmonic curvature and positive Sobolev constant. Assume that $L_2$ norms of Weyl curvature and traceless Ricci curvature are finite. We prove that $(M,g)$ is Einstein if $n \ge 5$ and $L_{n/2}$ norms of Weyl curvature and traceless Ricci curvature are small enough.

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Seongtag Kim. 2009-11-13. Rigidity of noncompact complete manifolds with harmonic curvature. https://arxiv.org/abs/0911.2694

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