RIGIDITY THEOREMS FOR COMPACT HYPERSURFACES IN LOCALLY SYMMETRIC RIEMANNIAN MANIFOLDS

Zhang Shicheng

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RIGIDITY THEOREMS FOR COMPACT HYPERSURFACES IN LOCALLY SYMMETRIC RIEMANNIAN MANIFOLDS

机译：局部对称黎曼歧管紧凑型超空间的刚性定理

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摘要

In this paper, we prove some rigidity theorems for compact hyper-surfaces without the constancy condition on the mean curvature or the scalar curvature in locally symmetric Riemannian manifolds.

机译：在本文中，我们在局部对称的黎曼歧管中没有对平均曲率或标量曲率的恒定条件来证明一定的刚性定理。

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来源
《Proceedings of the American Mathematical Society》 |2017年第10期|共8页
作者
Zhang Shicheng;
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作者单位

Jiangsu Normal Univ Sch Math &

Stat Xuzhou 221116 Jiangsu Peoples R China;

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原文格式 PDF
正文语种 eng
中图分类数学;
关键词
Locally symmetric; infinite fundamental group; Riemannian product;

机译：局部对称;无限基本组;riemananian产品;

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专利

1. RIGIDITY THEOREMS FOR COMPACT HYPERSURFACES IN LOCALLY SYMMETRIC RIEMANNIAN MANIFOLDS [J] . Zhang Shicheng Proceedings of the American Mathematical Society . 2017,第10期

机译：局部对称黎曼歧管紧凑型超空间的刚性定理
2. A Global Rigidity Theorem for the Length of Concircular Curvature Tensor on the Locally Conformally Symmetric Riemannian Manifold [J] . Shipei HU 数学研究及应用：英文版 . 2020,第002期

机译：局部保形对称黎曼流形上圆曲率张量长度的整体刚性定理
3. Prime geodesic theorem for compact even-dimensional locally symmetric Riemannian manifolds of strictly negative sectional curvature [J] . DZENAN GUSIC WSEAS Transactions on Mathematics . 2018,第Pta1期

机译：严格截面曲率的紧凑型偶数局部对称黎曼歧管的主要测距定理
4. A rigidity theorem for closed hypersurfaces in a symmetric space [C] . Shunjuan Cao, Zongwei Ma The Third International Workshop on Applied Matrix Theory（第三届国际矩阵分析与应用会议）论文集 . 2009

机译：对称空间中封闭超曲面的刚度定理
5. Compactness Theorems for Riemannian Manifolds with Boundary and Applications. [D] . Knox, Kenneth Steven. 2013

机译：具有边界和应用的黎曼流形的紧性定理。
6. Metric rigidity theorems on Hermitian locally symmetric spaces [O] . Ngaiming Mok 1986

机译：Hermitian局部对称空间上的度量刚性定理
7. Rigidity theorems of hypersurfaces in locally symmetric Riemannian manifold [O] . Shicheng Zhang, Baoqiang Wu 2013

机译：局部对称黎曼歧管的过度裂缝刚性定理
8. Spherical-Type Hypersurfaces in a Riemannian Manifold. [R] . Ezin, J. P., Rigoli, M. 1988

机译：黎曼流形中的球形超曲面。

RIGIDITY THEOREMS FOR COMPACT HYPERSURFACES IN LOCALLY SYMMETRIC RIEMANNIAN MANIFOLDS

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