Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Schwarzian derivative and conformal transformation on Finsler
  manifolds   Thurston, in 1986, discovered that the Schwarzian derivative has mysterious
properties similar to the curvature on a manifold. After his work, there are
several approaches to develop this notion on Riemannian manifolds. Here, a
tensor field is identified in the study of global conformal diffeomorphisms on
Finsler manifolds as a natural generalization of the Schwarzian derivative.
Then, a natural definition of a Mobius mapping on Finsler manifolds is given
and its properties are studied. In particular, it is shown that Mobius mappings
are mappings that preserve circles and vice versa. Therefore, if a forward
geodesically complete Finsler manifold admits a Mobius mapping, then the
indicatrix is conformally diffeomorphic to the Euclidean sphere $ S^{n-1}$ in $
\mathbb{R}^n $. In addition, if a forward geodesically complete absolutely
homogeneous Finsler manifold of scalar flag curvature admits a non-trivial
change of Mobius mapping, then it is a Riemannian manifold of constant
sectional curvature.

11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin