Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Product and anti-Hermitian structures on the tangent space   Noting that the complete lift of a Rimannian metric defined on a
differentiable manifold is not 0-homogeneous on the fibers of the tangent
bundle . In this paper we introduce a new lift which is 0-homogeneous. It
determines on slit tangent bundle a pseudo-Riemannian metric, which depends
only on the metric . We study some of the geometrical properties of this
pseudo-Riemannian space and define the natural almost complex structure and
natural almost product structure which preserve the property of homogeneity and
find some new results.

3
The categories of this paper are: physics
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom