Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finsleroids with three axes in dimension $N=3$   The Conclusive Theorem has been established to determine the dependence of
the three-axes positive-definite Finsleroid metric functions $F$ on the
Finsleroid azimuthal angle $\theta$ in the three-dimensional case $N=3$,
provided that the condition of the angle-separation in the involved
characteristic functions is implied. The complete set of algebraic and
differential equations is derived in all rigor which are necessary and
sufficient in order that the function $F$ belong to the class.
  It proves possible to solve the equations and obtain the explicit dependence
of the involved characteristic functions on the angle $\theta$.

29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol