Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: DDVV-type inequality for skew-symmetric matrices and Simons-type
  inequality for Riemannian submersions   In this paper, we will first derive a DDVV-type optimal inequality for real
skew-symmetric matrices, then we apply it to establish a Simons-type integral
inequality for Riemannian submersions with totally geodesic fibres and
Yang-Mills horizontal distributions. In this way, we show phenomenons of
duality between Submanifold geometry and Riemannnian submersion, particularly
between second fundamental form of a submanifold and integrability tensor of a
Riemannian submersion.

33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
7
The categories of this paper are: hep-th
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
3
The categories of this paper are: physics
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat
36
The categories of this paper are: cmp-lg
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat