Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A topological lower bound for the energy of a unit vector field on a
  closed Euclidean hypersurface   For a unit vector field on a closed immersed Euclidean hypersurface
$M^{2n+1}$, $n\geq 1$, we exhibit a nontrivial lower bound for its energy which
depends on the degree of the Gauss map of the immersion. When the hypersurface
is the unit sphere $\mathbb{S}^{2n+1}$, immersed with degree one, this lower
bound corresponds to a well established value from the literature. We introduce
a list of functionals $\mathcal{B}_k$ on a compact Riemannian manifold $M^{m}$,
$1\leq k\leq m$, and show that, when the underlying manifold is a closed
hypersurface, these functionals possess similar properties regarding the degree
of the immersion. In addition, we prove that Hopf flows minimize
$\mathcal{B}_n$ on $\mathbb{S}^{2n+1}$.

17
The categories of this paper are: q-fin
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess