Foliations by Spacelike Hypersurfaces on Lorentz Manifolds

被引：2

作者：

dos Santos Barreiro Chaves, Rosa Maria ^{[2
]}

da Silva, Euripedes Carvalho ^{[1
]}

机构：

[1] Inst Fed Educ Ciencia & Tecnol Ceara, Ave Parque Cent 1315, BR-61939140 Maracanau, Ceara, Brazil

[2] Univ Sao Paulo, Dept Matemat, Rua Matao 1010, BR-05508090 Sao Paulo, Brazil

来源：

RESULTS IN MATHEMATICS | 2020年 / 75卷 / 01期

关键词：

Foliations; hypersurfaces; lorentz manifolds; CONSTANT MEAN-CURVATURE;

D O I：

10.1007/s00025-020-1159-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work, we study the geometric properties of spacelike foliations by hypersurfaces on a Lorentz manifold. We find an equation that relates the foliation with the ambient manifold and applies it to investigate conditions for the leaves being totally umbilical or geodesic. Using the Maximum principle with the mentioned equation we obtain an obstruction for the existence of totally geodesic spacelike foliations in a spacetime with positive Ricci curvature on the direction N.

引用

页数：15

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