Spacelike metric foliations

被引：3

作者：

Walschap, G ^{[1
]}

机构：

[1] Univ Oklahoma, Dept Math, Norman, OK 73019 USA

来源：

JOURNAL OF GEOMETRY AND PHYSICS | 1999年 / 32卷 / 02期

关键词：

metric foliation; spacetime; Raychaudhuri equation;

D O I：

10.1016/S0393-0440(99)00021-2

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate spacelike metric foliations in lightlike complete spacetimes. When such a foliation satisfies the strong energy condition Ric(v)(e) greater than or equal to 0 for timelike vectors e, it must be totally geodesic, and the metric is of higher rank, in the sense that each point of the spacetime is contained inside a flat, totally geodesic, timelike rectangle. If in addition Ric(v)(a) = 0, then the metric is (at least locally) a product metric, with the leaves of the foliation tangent to one of the factors. (C) 1999 Elsevier Science B.V. All right reserved. Subj. Class.: Differential geometry; General relativity 1991 MSG: 53C12; 53C80; 83C75.

引用

页码：97 / 101

页数：5