Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The length of the shortest closed geodesics on a positively curved
  manifold   We give a metric characterization of the Euclidean sphere in terms of the
lower bound of the sectional curvature and the length of the shortest closed
geodesics.

7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
19
The categories of this paper are: eess
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
12
The categories of this paper are: nucl-th
8
The categories of this paper are: hep-ex
1
The categories of this paper are: cs
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg