Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finsleroid space with angle and scalar product   A systematic approach has been developed to encompass the Minkowski-type
extension of Euclidean geometry such that a one-vector anisotropy is permitted,
retaining simultaneously the concept of angle. For the respective geometry, the
Euclidean unit ball is to be replaced by the body which is convex and rotund
and is found on assuming that its surface (the indicatrix extending the unit
sphere) is a space of constant positive curvature. We have called the body the
Finsleroid in view of its intrinsic relationship with the metric function of
Finsler type.
  The main point of the present paper is the angle coming from geodesics
through the cosine theorem, the underlying idea being to derive the angular
measure from the solutions to the geodesic equation which prove to be
obtainable in simple explicit forms. The substantive items concern geodesics,
angle, scalar product, perpendicularity, and two-vector metric tensor. The
Finsleroid-space-associated one-vector Finslerian metric function admits in
quite a natural way an attractive two-vector extension.

0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
28
The categories of this paper are: alg-geom
21
The categories of this paper are: adap-org
30
The categories of this paper are: q-alg
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
1
The categories of this paper are: cs
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
11
The categories of this paper are: hep-lat