Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The curvature operator at the soul   We prove two splitting theorems, one topological, the other metric, for open
manifolds with nonnegative sectional curvature.

22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
15
The categories of this paper are: nucl-ex
20
The categories of this paper are: acc-phys
5
The categories of this paper are: gr-qc
12
The categories of this paper are: nucl-th
37
The categories of this paper are: supr-con
26
The categories of this paper are: bayes-an
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th