Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dependence of the Gauss-Codazzi equations and the Ricci equation of
  Lorentz surfaces   The fundamental equations of Gauss, Codazzi and Ricci provide the conditions
for local isometric embeddability. In general, the three fundamental equations
are independent for surfaces in Riemannian 4-manifolds. In contrast, we prove
in this article that for arbitrary Lorentz surfaces in Lorentzian Kaehler
surfaces the equation of Ricci is a consequence of the equations of Gauss and
Codazzi.

11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
24
The categories of this paper are: dg-ga
34
The categories of this paper are: chem-ph
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
22
The categories of this paper are: chao-dyn
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
9
The categories of this paper are: nlin