Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hom-Poisson-Nijenhuis structures on Hom-Lie algebroids and Hom-Dirac
  structures on Hom-Courant algebroids   In this paper, we develop the theory of Hom-Lie algebroids, Hom-Lie
bialgebroids and Hom-Courant algebroids introduced by Cai, Liu and Sheng.
Specifically, we introduce the notions of Hom-Poisson, Hom-Nijenhuis and
Hom-Poisson-Nijenhuis structures on a Hom-Lie algebroid and the notion of
Hom-Dirac structures on a Hom-Courant algebroid. We show that these structures
satisfy similar properties to structures non "Hom-"version. For example, there
exists the hierarchy of a Hom-Poisson-Nijenhuis structure and we have a
relation between Hom-Dirac structures and Maurer-Cartan type equation. Moreover
we show that there exists a one-to-one correspondence between the pairs
consisting of a Poisson structure on $M$ and a Poisson isomorphism for it.

19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
10
The categories of this paper are: q-bio
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
26
The categories of this paper are: bayes-an
29
The categories of this paper are: funct-an
16
The categories of this paper are: stat
18
The categories of this paper are: econ