Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Kahler-Einstein inspired anzatz for Spin(7) holonomy metrics and its
  solution   We construct propose an anzatz for Spin(7) metrics as an R-bundle over closed
G2 structures. These G2 structures are R3 bundles over 4-dimensional compact
quaternion Kahler spaces. The inspiration for the anzatz metric comes from the
Bryant-Salamon construction of G2 holonomy metrics and from the fact that the
twistor space of any compact quaternion Kahler space is Kahler-Einstein. The
reduction of the holonomy to a subgroup of Spin(7) gives non linear system
relating three unknown functions of one variable. We obtain a particular
solution and we find that the resulting metric is a Calabi-Yau cone over an
Einstein-Sassaki manifold which means that the holonomy is reduced to SU(4).
Another coordinate change show us that our metrics are hyperkahler cones known
as Swann bundles, thus the holonomy is reduced to Sp(2) and the cone is
tri-Sassakian. We revert our argument and state that the Swann bundle define a
closed G2 structure by reduction along an isometry. We calculate the torsion
classes for such structure explicitly.

17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
26
The categories of this paper are: bayes-an
16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc