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 | |
【 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.
【 授权许可】
Free
【 预 览 】
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10_1016_j_geomphys_2010_11_003.pdf | 210KB | download |