Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Normal curvature of pseudo-umblical submanifolds in a sphere   Let M be a compact pseudo-umbilical submanifold of the unit sphere S. In the
present note, it is shown that if the normal curvature, scalar curvature S and
square of the length of second fundamental form satisfy certain conditions,
then M is totally geodesic.

22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
24
The categories of this paper are: dg-ga
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
32
The categories of this paper are: atom-ph
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph