A functional expression for the curvature of hyperdimensional Riemannian spaces
Abstract
Analogously to the concept of a curvature of curve and surface, in the differential geometry, in the main part of this paper the concept of the curvature of the hyperdimensional vector spaces of Riemannian metric is generally defined. The defined concept of the curvature of Riemannian spaces of higher dimensions M: M>1, in the further text of the paper, is functional related to the fundamental parameters of an internal geometry of space, more exactly, to components of RiemannChristoffel's tensor of curvature. At the end, analogously to the concept of lines of curvature in the differential geometry, the concept of subspaces of curvature of Riemannian hyperdimensional vector spaces is also generally defined.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 April 2000
 arXiv:
 arXiv:math/0004153
 Bibcode:
 2000math......4153S
 Keywords:

 Mathematics  Differential Geometry;
 53A35 (Primary);
 53A45 (Secondary)
 EPrint:
 LaTeX2e, 11 pages, submitted to Transactions of the AMS