학술논문
Space-time of class one
Document Type
Journal Article
Author
Source
General Relativity and Gravitation; (USA); 21:8
Subject
Language
English
ISSN
0001-7701
Abstract
The authors study space-times embedded in E{sub 5} (that means, pseudo-euclidean five-dimensional spaces) in the intrinsic rigidity case, i.e., when the second fundamental form b{sub if} can be determined by the internal geometry of the four-dimensional Riemannian space R{sub 4}. They write down the Gauss and Codazzi equations determining the local isometric embedding of R{sub 4} in E{sub 5} and give some consequences of it. They prove that when there exists intrinsic rigidity, then b{sub if} is a linear combination of the metric and Ricci tensor; it is given some applications for the de Sitter and Einstein models.