Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Harmonicity and Minimality of vector fields on four-dimensional
  Lorentzian lie groups   We consider four dimensional lie groups equipped with left invariant
Lorentzian Einstein metrics, and determine the harmonicity properties of vector
fields on these spaces. In some cases, all these vector fields are critical
points for the energy functional restricted to vector fields. We also classify
vector fields defining harmonic maps, and calculate explicitly the energy of
these vector fields. Then we study the minimality of critical points for the
energy functional.

12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg