  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 hyper-dimensional 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 Riemann-Christoffel's tensor of curvature. At the
end, analogously to the concept of lines of curvature in the differential
geometry, the concept of sub-spaces of curvature of Riemannian
hyper-dimensional vector spaces is also generally defined.
