Instruct: Identify the main and secondary category of Arxiv papers based on the titles
Query: Submanifolds of codimension two attaining equality in an extrinsic
  inequality
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
23
The categories of this paper are: solv-int
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga