Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Invariant surfaces with coordinate finite-type Gauss map in simply
  isotropic space   We consider the extrinsic geometry of surfaces in simply isotropic space, a
three-dimensional space equipped with a rank 2 metric of index zero. Since the
metric is degenerate, a surface normal cannot be unequivocally defined based on
metric properties only. To understand the contrast between distinct choices of
an isotropic Gauss map, here we study surfaces with a Gauss map whose
coordinates are eigenfunctions of the surface Laplace-Beltrami operator. We
take into account two choices, the so-called minimal and parabolic normals, and
show that when applied to simply isotropic invariant surfaces the condition
that the coordinates of the corresponding Gauss map are eigenfunctions leads to
planes, certain cylinders, or surfaces with constant isotropic mean curvature.
Finally, we also investigate (non-necessarily invariant) surfaces with harmonic
Gauss map and show this characterizes constant mean curvature surfaces.

25
The categories of this paper are: patt-sol
9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
15
The categories of this paper are: nucl-ex
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph