Quasi-Euclidean space
From Encyclopedia of Mathematics
A 
-dimensional space in which each direction given at a point of it can be included in a field the directions of which can be transferred parallelly along any path (that is, a quasi-Euclidean space admits an absolute parallelism). The geodesic lines of a quasi-Euclidean space are partitioned into 
families of vector lines of fields of absolutely parallel directions, where each such family forms with three others a constant cross ratio:
 |
where 
is the angular direction coefficient. Each family of geodesics is defined in terms of three constants by a first-order equation:
 |
References
| [1] | A.P. Norden, "Spaces with an affine connection" , Nauka , Moscow-Leningrad (1976) (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:
Quasi-Euclidean space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-Euclidean_space&oldid=32052
Quasi-Euclidean space. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Quasi-Euclidean_space&oldid=32052
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article