Semi-pseudo-Riemannian space
From Encyclopedia of Mathematics
A manifold with a degenerate indefinite metric. The semi-pseudo-Riemannian manifold 
is defined as an 
-dimensional manifold with coordinates 
in which there are given 
line elements
 |
where 
; 
; and where the index of the quadratic form 
is 
. The line element 
is defined for those vectors for which all components with indices smaller than 
or larger than 
vanish. If 
, a semi-pseudo-Riemannian space is a semi-Riemannian space. The spaces 
and 
are quasi-Riemannian spaces. The basic concepts of differential geometry (for example, curvature) are defined in semi-pseudo-Riemannian spaces similarly to Riemannian spaces (see [1]).
References
| [1] | B.A. Rozenfel'd, "Non-Euclidean spaces" , Moscow (1969) (In Russian) |
Comments
References
| [a1] | B.A. [B.A. Rozenfel'd] Rosenfel'd, "A history of non-euclidean geometry" , Springer (1988) (Translated from Russian) |
How to Cite This Entry:
Semi-pseudo-Riemannian space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-pseudo-Riemannian_space&oldid=18344
Semi-pseudo-Riemannian space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Semi-pseudo-Riemannian_space&oldid=18344
This article was adapted from an original article by D.D. Sokolov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article