Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Splitting and gluing constructions for geodesically equivalent
  pseudo-Riemannian metrics   Two metrics $g $ and $\bar g$ are geodesically equivalent, if they share the
same (unparameterized) geodesics. We introduce two constructions that allow one
to reduce many natural problems related to geodesically equivalent metrics,
such as the classification of local normal forms and the Lie problem (the
description of projective vector fields), to the case when the (1,1)-tensor
$G^i_j:= g^{ik} \bar g_{kj}$ has one real eigenvalue, or two complex conjugate
eigenvalues, and give first applications. As a part of the proof of the main
result, we generalize Topalov-Sinjukov (hierarchy) Theorem for
pseudo-Riemannian metrics

19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
11
The categories of this paper are: hep-lat
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
36
The categories of this paper are: cmp-lg
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph