Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Codazzi tensors on a hyperbolic surface and flat Lorentzian geometry   Using global considerations, Mess proved that the moduli space of globally
hyperbolic flat Lorentzian structures on $S\times\mathbb{R}$ is the tangent
bundle of the Teichm\"uller space of $S$, if $S$ is a closed surface. One of
the goals of this paper is to deepen this surprising occurrence and to make
explicit the relation between the Mess parameters and the embedding data of any
Cauchy surface. This relation is pointed out by using some specific properties
of Codazzi tensors on hyperbolic surfaces. As a by-product we get a new
Lorentzian proof of Goldman's celebrated result about the coincidence of the
Weil-Petersson symplectic form and the Goldman pairing.
  In the second part of the paper we use this machinery to get a classification
of globally hyperbolic flat space-times with particles of angles in $(0,2\pi)$
containing a uniformly convex Cauchy surface. The analogue of Mess' result is
achieved showing that the corresponding moduli space is the tangent bundle of
the Teichm\"uller space of a punctured surface. To generalize the theory in the
case of particles, we deepen the study of Codazzi tensors on hyperbolic
surfaces with cone singularities, proving that the well-known decomposition of
a Codazzi tensor in a harmonic part and a trivial part can be generalized in
the context of hyperbolic metrics with cone singularities.

22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
10
The categories of this paper are: q-bio
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph