Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: $HS_{r}$-valued Gauss maps and umbilic spacelike surfaces of codimension
  two   To study spacelike surfaces of codimension two in the Lorentz-Minkowski space
$\Bbb R^{n+1}_1,$ we construct a pair of maps whose values are in
$HS_r:=H_+^n(\textbf v,1)\cap \{x_{n+1}=r\},$ called $\textbf n_r^{\pm}$-Gauss
maps. It is showed that they are well-defined and useful to study practically
flat as well as umbilic spacelike surfaces of codimension two in $\Bbb
R^{n+1}_1.$

31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
7
The categories of this paper are: hep-th