Rigidity for closed manifolds with positive curvature

被引：0

作者：

Changyu Xia

机构：

[1] Universidade de Brasília,Departamento de Matemática

[2] MPI for Mathematics in the Sciences,undefined

来源：

Annals of Global Analysis and Geometry | 2009年 / 36卷

关键词：

Rigidity; Closed manifolds; Sectional curvature; Conjugate locus; 53C20;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let M be an n-dimensional complete connected Riemannian manifold with sectional curvature sec(M) ≥ 1 and radius rad(M) > π/2. In this article, we show that M is isometric to a round n-sphere if for any x ∈ M, the first conjugate locus of x is a single point and if M contains a geodesic loop of length 2 · rad(M). We also show that the same conclusion is true if the conjugate value function at any point of M is a constant function.

引用

页码：105 / 110

页数：5

共 20 条

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Moore J.D.(undefined)undefined undefined undefined undefined-undefined

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[18]

Yang C.T.(undefined)undefined undefined undefined undefined-undefined

[19]

Xia C.(undefined)undefined undefined undefined undefined-undefined

[20]

Xia C.(undefined)undefined undefined undefined undefined-undefined

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