Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal forms for pseudo-Riemannian 2-dimensional metrics whose geodesic
  flows admit integrals quadratic in momenta   We discuss pseudo-Riemannian metrics on 2-dimensional manifolds such that the
geodesic flow admits a nontrivial integral quadratic in velocities. We
construct local normal forms of such metrics. We show that these metrics have
certain useful properties similar to those of Riemannian Liouville metrics,
namely: 1) they admit geodesically equivalent metrics; 2) one can use them to
construct a big family of natural systems admitting integrals quadratic in
momenta; 3) the integrability of such systems can be generalized to the quantum
setting; 4) these natural systems are integrable by quadratures.

25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
1
The categories of this paper are: cs
33
The categories of this paper are: plasm-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
5
The categories of this paper are: gr-qc
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The categories of this paper are: dg-ga
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The categories of this paper are: stat