Rigidity of complete manifolds with parallel Cotton tensor
Rigidity of complete manifolds with parallel Cotton tensor
复制标题
具有平行 Cotton 张量的完整流形的刚度
DOI：
10.1007/s00013-017-1047-y
复制
发表时间：
2017
影响因子：
0.6
通讯作者：
Fang Shouwen
中科院分区：
文献类型：
--
作者：
Chu Yawei;Fang Shouwen
The aim of this paper is to show some rigidity results for complete Riemannian manifolds with parallel Cotton tensor. In particular, we prove that any compact manifold of dimensionwith parallel Cotton tensor and positive constant scalar curvature is isometric to a finite quotient ofunder a pointwise or integral pinching condition. Moreover, a rigidity theorem for stochastically complete manifolds with parallel Cotton tensor is also given. The proofs rely mainly on curvature elliptic estimates and the weak maximum principle.
