Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Natural Connection with Totally Skew-Symmetric Torsion on Riemannian
  Almost Product Manifolds   On a Riemannian almost product manifold $(M,P,g)$ we consider a linear
connection preserving the almost product structure $P$ and the Riemannian
metric $g$ and having a totally skew-symmetric torsion. We determine the class
of the manifolds $(M,P,g)$ admitting such a connection and prove that this
connection is unique in terms of the covariant derivative of $P$ with respect
to the Levi-Civita connection. We find a necessary and sufficient condition the
curvature tensor of the considered connection to have similar properties like
the ones of the K\"ahler tensor in Hermitian geometry. We pay attention to the
case when the torsion of the connection is parallel. We consider this
connection on a Riemannian almost product manifold $(G,P,g)$ constructed by a
Lie group $G$.

16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
35
The categories of this paper are: mtrl-th
34
The categories of this paper are: chem-ph
11
The categories of this paper are: hep-lat
4
The categories of this paper are: cond-mat
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
13
The categories of this paper are: quant-ph
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph