Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hypersurfaces in space forms satisfying the condition $L_kx=Ax+b$   We study hypersurfaces either in the sphere \s{n+1} or in the hyperbolic
space \h{n+1} whose position vector $x$ satisfies the condition $L_kx=Ax+b$,
where $L_k$ is the linearized operator of the $(k+1)$-th mean curvature of the
hypersurface for a fixed $k=0,...,n-1$, $A\in\R{(n+2)\times (n+2)}$ is a
constant matrix and $b\in\R{n+2}$ is a constant vector. For every $k$, we prove
that when $A$ is self-adjoint and $b=0$, the only hypersurfaces satisfying that
condition are hypersurfaces with zero $(k+1)$-th mean curvature and constant
$k$-th mean curvature, and open pieces of standard Riemannian products of the
form $\s{m}(\sqrt{1-r^2})\times\s{n-m}(r)\subset\s{n+1}$, with $0<r<1$, and
$\h{m}(-\sqrt{1+r^2})\times\s{n-m}(r)\subset\h{n+1}$, with $r>0$. If $H_k$ is
constant, we also obtain a classification result for the case where $b\neq 0$.

30
The categories of this paper are: q-alg
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
29
The categories of this paper are: funct-an
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
33
The categories of this paper are: plasm-ph