Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Berwald metrics constructed by Chevalley's polynomials   Berwald metrics are particular Finsler metrics which still have linear
Berwald connections. Their complete classification is established in an earlier
work, [Sz1], of this author. The main tools in these classification are the
Simons-Berger holonomy theorem and the Weyl-group theory. It turnes out that
any Berwald metric is a perturbed-Cartesian product of Riemannian, Minkowski,
and such non-Riemannian metrics which can be constructed on irreducible
symmetric manifolds of $rank > 1$. The existence of these metrics are well
established by the above theories.
  The present paper has several new features. First, the Finsler functions of
Berwald manifolds are explicitly described by the Chevalley polynomials. New
results are also the complete lists of reversible (d(x,y)=d(y,x)) resp.
irreversible ($d(x,y)\not =d(y,x)$) Berwald metrics. The Cartan symmetric
Finsler manifolds are also completely determined. The paper is concluded by
proving that a Berwald metric is uniquely determined by the Minkowski metric
induced on an arbitrarily fixed maximal totalgeodesic flat submanifold (Cartan
flat). Moreover, any two Cartan flats are isometric.

23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph