Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Variational problems for integral invariants of the second fundamental
  form of a map between pseudo-Riemannian manifolds   We study variational problems for integral invariants, which are defined as
integrations of invariant functions of the second fundamental form, of a smooth
map between pseudo-Riemannian manifolds. We derive the first variational
formulae for integral invariants defined from invariant homogeneous polynomials
of degree two. Among these integral invariants, we show that the Euler-Lagrange
equation of the Chern-Federer energy functional is reduced to a second order
PDE. Then we give some examples of Chern-Federer submanifolds in Riemannian
space forms.

35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph