2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59067Analogously 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.LaTeX2e, 11 pages, submitted to Transactions of the AMSDifferential Geometry53A35 (Primary); 53A45 (Secondary)text