Frontiers of Mathematics in China >

2012 , Vol. 7 >Issue 1: 19 - 27

DOI: https://doi.org/10.1007/s11464-012-0168-7

RESEARCH ARTICLE

Complete noncompact manifolds with harmonic curvature

  • Yawei CHU , 1,2
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  • 1. Department of Mathematics, Zhengzhou University, Zhengzhou 450001, China
  • 2. School of Mathematics and Computational Science, Fuyang University, Fuyang 236037, China

Received date: 15 Sep 2010

Accepted date: 15 Oct 2011

Published date: 01 Feb 2012

Copyright

2014 Higher Education Press and Springer-Verlag Berlin Heidelberg
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Abstract

Let (Mn, g) be an n-dimensional complete noncompact Riemannian manifold with harmonic curvature and positive Sobolev constant. In this paper, by employing an elliptic estimation method, we show that (Mn, g) is a space form if it has sufficiently small Ln/2-norms of trace-free curvature tensor and nonnegative scalar curvature. Moreover, we get a gap theorem for (Mn, g) with positive scalar curvature.

Key words： Harmonic curvature; trace-free curvature tensor; space form

Cite this article

Yawei CHU . Complete noncompact manifolds with harmonic curvature[J]. Frontiers of Mathematics in China, 2012 , 7(1) : 19 -27 . DOI: 10.1007/s11464-012-0168-7

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