期刊论文详细信息
JOURNAL OF GEOMETRY AND PHYSICS 卷:61
A rigidity theorem for complete noncompact Bach-flat manifolds
Article
Chu, Yawei1,2 
[1] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China
[2] Fuyang Univ, Sch Math & Computat Sci, Fuyang 236041, Anhui, Peoples R China
关键词: Bach-flat;    Rigidity;    Trace-free curvature tensor;    Space form;   
DOI  :  10.1016/j.geomphys.2010.11.003
来源: Elsevier
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【 摘 要 】

Let (M-4, g) be a four-dimensional complete noncompact Bach-flat Riemannian manifold with positive Yamabe constant. In this paper, we show that (M-4, g) has a constant curvature if it has a nonnegative constant scalar curvature and sufficiently small L-2-norm of trace-free Riemannian curvature tensor. Moreover, we get a gap theorem for (M-4, g) with positive scalar curvature. (C) 2010 Elsevier B.V. All rights reserved.

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