Rigidity of noncompact complete manifolds with harmonic curvature

Seongtag Kim

Rigidity of noncompact complete manifolds with harmonic curvature

Differential Geometry 2010-01-15 v2 General Relativity and Quantum Cosmology

Authors: Seongtag Kim

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.

Keywords

harmonic curvature noncompact complete manifold Einstein manifold Weyl curvature traceless Ricci curvature Sobolev constant

Cite

@article{arxiv.0911.2694,
  title  = {Rigidity of noncompact complete manifolds with harmonic curvature},
  author = {Seongtag Kim},
  journal= {arXiv preprint arXiv:0911.2694},
  year   = {2010}
}

Comments

11 page, corrections + updated results

Related papers

View all related →