Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Characterization of hypersurfaces in four dimensional product spaces via
  two different Spin$^c$ structures   The Riemannian product $\mathbb M_1(c_1) \times \mathbb M_2(c_2)$, where
$\mathbb M_i(c_i)$ denotes the $2$-dimensional space form of constant sectional
curvature $c_i \in \mathbb R$, has two different Spin$^c$ structures carrying
each a parallel spinor. The restriction of these two parallel spinor fields to
a $3$-dimensional hypersurface $M$ characterizes the isometric immersion of $M$
into $\mathbb M_1(c_1) \times \mathbb M_2(c_2)$. As an application, we prove
that totally umbilical hypersurfaces of $\mathbb M_1(c_1) \times \mathbb
M_1(c_1)$ and totally umbilical hypersurfaces of $\mathbb M_1(c_1) \times
\mathbb M_2(c_2)$ ($c_1 \neq c_2$) having a local structure product, are of
constant mean curvature.

31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc