Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A functional expression for the curvature of hyper-dimensional
  Riemannian spaces   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.

33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
19
The categories of this paper are: eess
24
The categories of this paper are: dg-ga
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int