Rigidity of noncompact complete manifolds with harmonic curvature

Details Rigidity of noncompact complete manifolds with harmonic curvature Rigidity of noncompact complete manifolds with harmonic curvature

2009-11-13

arxiv.org/abs/0911.2694v2

Mathematics

Differential Geometry

11 page, corrections + updated results

Scientific paper

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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