Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Totally umbilical hypersurfaces of manifolds admitting a unit Killing
  field   We prove that a Riemannian product of type M x R (where R denotes the
Euclidean line) admits totally umbilical hypersurfaces if and only if M has
locally the structure of a warped product and we give a complete description of
the totally umbilical hypersurfaces in this case. Moreover, we give a necessary
and sufficient condition under which a Riemannian three-manifold carrying a
unit Killing field admits totally geodesic surfaces and we study local and
global properties of three-manifolds satisfying this condition.

36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
24
The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
26
The categories of this paper are: bayes-an
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
37
The categories of this paper are: supr-con