A functional expression for the curvature of hyper-dimensional Riemannian spaces
(Lobachevskii Journal of Mathematics, Volume VII)
Analogously to a notion of curvature of a curve and a surface, in the differential geometry, in the main part of this paper the notion of curvature of hyper-dimensional vector spaces of Riemannian metric is generally defined. The defined notion of curvature of Riemannian spaces of higher dimensions M: M≥ 2, in the further text of the paper, is functional related to the fundamental parameters of internal geometry of a space, more exactly, to components of Riemann-Christoffel's curvature tensor. At the end, analogously to a notion of lines of a curvature in the differential geometry, the notion of sub-spaces of curvature of Riemannian hyper-dimensional vector spaces is also generally defined.