A rigidity theorem for complete noncompact Bach-flat manifolds

被引：10

作者：

Chu, Yawei ^{[1
,2
]}

机构：

[1] Zhengzhou Univ, Dept Math, Zhengzhou 450052, Peoples R China

[2] Fuyang Univ, Sch Math & Computat Sci, Fuyang 236041, Anhui, Peoples R China

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 2011年 / 61卷 / 02期

关键词：

Bach-flat; Rigidity; Trace-free curvature tensor; Space form; DEFORMATION;

D O I：

10.1016/j.geomphys.2010.11.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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.

引用

页码：516 / 521

页数：6

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