Geodesic
A functional expression for the curvature of hyper-dimensional Riemannian spaces
Lobachevskii journal of mathematics, Tome 7 (2000), pp. 31-42.

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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 $M\colon M\ge 2$, 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.
Keywords: space, curvature of space, sub-space of curvature. 
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     title = {A functional expression for the curvature of hyper-dimensional {Riemannian} spaces},
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B. Sarić. A functional expression for the curvature of hyper-dimensional Riemannian spaces. Lobachevskii journal of mathematics, Tome 7 (2000), pp. 31-42. http://geodesic.mathdoc.fr/item/LJM_2000_7_a2/