Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Finsler Manifolds with Nonpositive Flag Curvature and Constant
  S-curvature   The flag curvature is a natural extension of the sectional curvature in
Riemannian geometry, and the S-curvature is a non-Riemannian quantity which
vanishes for Riemannian metrics. There are (incomplete) non-Riemannian Finsler
metrics on an open subset in R^n with negative flag curvature and constant
S-curvature. In this paper, we are going to show a global rigidity theorem that
every Finsler metric with negative flag curvature and constant S-curvature must
be Riemannian if the manifold is compact. We also study the nonpositive flag
curvature case.

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The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
24
The categories of this paper are: dg-ga
37
The categories of this paper are: supr-con
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The categories of this paper are: stat
14
The categories of this paper are: math-ph
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
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The categories of this paper are: cs
35
The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat