Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ricci Solitons on Pseudo-Riemannian Hypersurfaces of 4-dimensional
  Minkowski space   In this article, we get classification theorems for a Ricci soliton on the
pseudo-Riemannian hypersurface of the Minkowski space $\mathbb{E}^4_1$ taking
the potential vector field as the tangent component of the position vector of
the pseudo-Riemannian hypersurface, denoted by $(M,g,{\bf x}^T,\lambda)$ in
both Riemannian and Lorentzian settings. First, we obtain the necessary and
sufficient condition that a pseudo-Riemannian hypersurface $(M,g)$ in
$\mathbb{E}^4_1$ admits a Ricci soliton $(M,g,{\bf x}^T,\lambda)$. In each of
the form of the shape operator of a pseudo-Riemannian hypersurface, we obtain
characterization a Ricci soliton on a pseudo-Riemannian hypersurface. More
precisely, we show that totally umbilical hypersurfaces, hyperbolic and a
pseudo-spherical cylinder in $\mathbb{E}^4_1$ is a shrinking Ricci soliton
whose the potential vector field is the tangent part of the position vector.
Furthermore, we conclude that there exists only a shrinking Ricci soliton on a
Lorentzian isoparametric hypersurface in $\mathbb{E}^4_1$ with
nondiagonalizable shape operator whose the minimal polynomial has double real
roots.

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The categories of this paper are: cs
16
The categories of this paper are: stat
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
23
The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat