Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Principal torus bundles of Lorentzian S-manifolds and the {\phi}-null
  Osserman condition   The main result we give in this brief note relates, under suitable
hypotheses, the {\phi}-null Osserman, the null Osserman and the classical
Osserman conditions to each other, via semi-Riemannian submersions as
projection maps of principal torus bundles arising from a Lorentzian
S-manifold.

27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
31
The categories of this paper are: ao-sci
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th