On locally convex hypersurfaces in Hadamard manifolds

被引：4

作者：

Borisenko, AA ^{[1
]}

机构：

[1] Kharkov State Univ, UA-310077 Kharkov, Ukraine

来源：

MATHEMATICAL NOTES | 2000年 / 67卷 / 3-4期

关键词：

Hadamard manifold; compact connected manifold; convex hypersurface; locally convex immersion; immersion regular of class C-2; second quadratic form;

D O I：

10.1007/BF02676397

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Locally convex compact hypersurfaces immersed in a hollow simply connected Riemannian space of nonpositive sectional curvature are considered. They are proved to be convex hypersurfaces homeomorphic to the sphere. A similar result for immersed hypersurfaces with nonpositive definite second quadratic form of rank no smaller than one is obtained.

引用

页码：425 / 432

页数：8

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