Izu Vaisman
A Lecture on Poisson-Nijenhuis Structures
The paper is published: in C. Albert et. al. (eds) "Integrable systems and foliations. Feuilletages et systemes integrables. Papers from a colloquium, Montpellier, France, May 22--26, 1995" Prog. Math. 145 Birkhäuser (1997), 169-185

MSC:

58F05 Hamiltonian and Lagrangian systems; symplectic geometry, See also {70Hxx, 81S10}

Abstract: This is an expository paper. In it,
the Poisson-Nijenhuis structures are motivated and defined
in the general algebraic framework of Gel'fand and Dorfman.
Then, in the particular case of Lie algebroids and
differentiable manifolds, the Poisson-Nijenhuis structures
are related to the notion of a complementary
$2$-form, introduced and studied by the author in \cite{V2},
and several examples of complementary forms and
Poisson-Nijenhuis manifolds are given.

Keywords: Poisson-Nijenhuis structure, complementary 2-Form