Some Rigidity Properties for Manifolds with Constant k-Curvature of Modified Schouten Tensor

被引：5

作者：

Bo, Leyang ^{[1
]}

Sheng, Weimin ^{[1
]}

机构：

[1] Zhejiang Univ, Sch Math Sci, Hangzhou 310027, Peoples R China

来源：

JOURNAL OF GEOMETRIC ANALYSIS | 2019年 / 29卷 / 03期

关键词：

Rigidity; Modified Schouten tensor; k-Curvature; Locally conformally flat; FULLY NONLINEAR EQUATIONS; YAMABE PROBLEM; HYPERSURFACES;

D O I：

10.1007/s12220-018-0097-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the rigidity problem on closed locally conformally flat manifolds with constant k-curvature or constant quotient curvature. We prove that such manifolds must have constant sectional curvature under the assumption that the manifolds have positive sectional curvature. The same result is also held on closed locally conformally flat manifolds with totally geodesic boundary.

引用

页码：2862 / 2887

页数：26

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