Characterizations of Umbilic Points of Isometric Immersions in Riemannian and Lorentzian Manifolds

被引：0

作者：

Caballero, Magdalena ^{[1
]}

Maria Rubio, Rafael ^{[1
]}

机构：

[1] Univ Cordoba, Dept Matemat, Campus Rabanales, E-14071 Cordoba, Spain

来源：

TAIWANESE JOURNAL OF MATHEMATICS | 2016年 / 20卷 / 05期

关键词：

Riemannian and Lorentzian manifolds; Spacelike and timelike submanifolds; Umbilic point; Submanifold totally geodesic at a point; Mean curvature vector field; Sphere; Hyperbolic space; CONSTANT MEAN-CURVATURE; SPACELIKE HYPERSURFACES; SITTER SPACE; CIRCLES;

D O I：

10.11650/tjm.20.2016.7383

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Several characterizations of umbilic points of submanifolds in arbitrary Riemannian and Lorentzian manifolds are given. As a consequence, we obtain new characterizations of spheres in the Euclidean space and of hyperbolic spaces in the Lorentz-Minkowski space. We also prove the Lorentzian version of a classical result by Cartan.

引用

页码：1041 / 1052

页数：12

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