Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On a Class of Two-Dimensional Singular Douglas and Projectively flat
  Finsler Metrics   Singular Finsler metrics, such as Kropina metrics and $m$-Kropina metrics,
have a lot of applications in the real world. In this paper, we study a class
of two-dimensional singular Finsler metrics defined by a Riemann metric
$\alpha$ and 1-form $\beta$, and we characterize those which are Douglasian or
locally projectively flat by some equations. It shows that the main class
induced is an $m$-Kropina metric plus a linear part on $\beta$. For this class,
the local structure of Douglasian or (in part) projectively flat case is
determined, and in particular we show that a Kropina metric is always
Douglasian and a Douglas $m$-Kropina metric with $m\ne -1$ is locally
Minkowskian. It indicates that the two-dimensional case is quite different from
the higher dimensional ones.

12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
1
The categories of this paper are: cs