Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Intrinsic and extrinsic geometry of hypersurfaces in $\mathbb{S}^n
  \times \mathbb{R}$ and $\mathbb{H}^n \times \mathbb{R}$   In this paper, geometric characterizations of conformally flat and radially
flat hypersurfaces in $\mathbb{S}^n \times \mathbb{R}$ and $\mathbb{H}^n \times
\mathbb{R}$ are given by means of their extrinsic geometry. Under suitable
conditions on the shape operator, we classify conformally flat hypersurfaces in
terms of rotation hypersurfaces. In addition, a close relation between radially
flat hypersurfaces and semi-parallel hypersurfaces is established. These
results lead to geometric descriptions of hypersurfaces with special intrinsic
structures, such as Einstein metrics, Ricci solitons and hypersurfaces with
constant scalar curvature.

29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
7
The categories of this paper are: hep-th
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int