Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Locally convex surfaces immersed in a Killing submersion   We generalize Hadamard-Stoker-Currier Theorems for surfaces immersed in a
Killing submersion over a strictly Hadamard surface whose fibers are the
trajectories of a unit Killing field. We prove that every complete surface
whose principal curvatures are greater than a certain function (depending on
the ambient manifold) at each point, must be properly embedded, homeomorphic to
the sphere or to the plane and, in the latter case, we study the behavior of
the end.

3
The categories of this paper are: physics
26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
0
The categories of this paper are: hep-ph
28
The categories of this paper are: alg-geom
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int