Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Weierstrass Representations of Lorentzian Minimal Surfaces in $\mathbb
  R^4_2$   The minimal Lorentzian surfaces in $\mathbb{R}^4_2$ whose first normal space
is two-dimensional and whose Gauss curvature $K$ and normal curvature
$\varkappa$ satisfy $K^2-\varkappa^2 >0$ are called minimal Lorentzian surfaces
of general type. These surfaces admit canonical parameters and with respect to
such parameters are determined uniquely up to a motion in $\mathbb{R}^4_2$ by
the curvatures $K$ and $\varkappa$ satisfying a system of two natural PDEs. In
the present paper we study minimal Lorentzian surfaces in $\mathbb{R}^4_2$ and
find a Weierstrass representation with respect to isothermal parameters of any
minimal surface with two-dimensional first normal space. We also obtain a
Weierstrass representation with respect to canonical parameters of any minimal
Lorentzian surface of general type and solve explicitly the system of natural
PDEs expressing any solution to this system by means of four real functions of
one variable.

32
The categories of this paper are: atom-ph
5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
8
The categories of this paper are: hep-ex
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph