Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the scalar curvature of hypersurfaces in spaces with a Killing field   We consider compact hypersurfaces in an $(n+1)$-dimensional either Riemannian
or Lorentzian space $N^{n+1}$ endowed with a conformal Killing vector field.
For such hypersurfaces, we establish an integral formula which, especially in
the simpler case when $N=M^n\times R$ is a product space, allows us to derive
some interesting consequences in terms of the scalar curvature of the
hypersurface. For instance, when $n=2$ and $M^2$ is either the sphere
$\mathbb{S}^2$ or the real projective plane $\mathbb{RP}^2$, we characterize
the slices of the trivial totally geodesic foliation $M^2\times\{t\}$ as the
only compact two-sided surfaces with constant Gaussian curvature in the
Riemannian product $M^2\times\mathbb{R}$ such that its angle function does not
change sign. When $n\geq 3$ and $M^n$ is a compact Einstein Riemannian manifold
with positive scalar curvature, we also characterize the slices as the only
compact two-sided hypersurfaces with constant scalar curvature in the
Riemannian product $M^n\times\mathbb{R}$ whose angle function does not change
sign. Similar results are also established for spacelike hypersurfaces in a
Lorentzian product $\mathbb{M}\times\mathbb{R}_1$.

8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
14
The categories of this paper are: math-ph
0
The categories of this paper are: hep-ph
22
The categories of this paper are: chao-dyn
26
The categories of this paper are: bayes-an
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph