Complete noncompact manifolds with harmonic curvature

被引：7
|
作者：
Chu, Yawei [1 ,2 ]
机构：
[1] Zhengzhou Univ, Dept Math, Zhengzhou 450001, Peoples R China
[2] Fuyang Univ, Sch Math & Computat Sci, Fuyang 236037, Peoples R China
来源：
FRONTIERS OF MATHEMATICS IN CHINA | 2012年 / 7卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Harmonic curvature; trace-free curvature tensor; space form; FLAT; DEFORMATION;
D O I：
10.1007/s11464-012-0168-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let (M (n) , 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 (M (n) , g) is a space form if it has sufficiently small L (n/2)-norms of trace-free curvature tensor and nonnegative scalar curvature. Moreover, we get a gap theorem for (M (n) , g) with positive scalar curvature.
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页码：19 / 27
页数：9
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