Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Powers of the space forms curvature operator and geodesics of the
  tangent bundle   It is well-known that if a curve is a geodesic line of the tangent (sphere)
bundle with Sasaki metric of a locally symmetric Riemannian manifold then the
projected curve has all its geodesic curvatures constant. In this paper we
consider the case of tangent (sphere) bundle over the real, complex and
quaternionic space form and give a unified proof of the following property: all
geodesic curvatures of projected curve are zero starting from k_3,k_6 and
k_{10} for the real, complex and quaternionic space formes respectively.

13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
15
The categories of this paper are: nucl-ex
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
37
The categories of this paper are: supr-con
6
The categories of this paper are: astro-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
23
The categories of this paper are: solv-int