##
*Branko Saric*

A functional expression for the curvature of

hyper-dimensional Riemannian spaces

*( Lobachevskii Journal of Mathematics,
Vol.7, pp.31-42 )*

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 \textit{Riemannian} metric is generally
defined. The defined notion of curvature of \textit{Riemannian} spaces
of higher dimensions $M$\textit{:}$\,M\geq 2$, 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 \textit{% 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
\textit{Riemannian} hyper-dimensional vector spaces is also generally defined.

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