Full paper in PDF format:
$%A. Awane, Generalized polarized manifolds, Rev. Mat. Complut. 21 (2007), no. 1, 251–264.%$

Generalized Polarized Manifolds
Azzouz AWANE
Equipe de Géométrie Différentielle et Application
Faculté des Sciences Ben M’sik
B.P. 7955. Boulevard Driss Harti
Casablanca — Maroc
a.awane@yahoo.fr

Received: February 8, 2007
Accepted: October 8, 2007

ABSTRACT

We introduce and develop the notion of generalized Poisson manifolds and analyze their main properties. Several generalized Hamiltonian maps for polarized Poisson manifolds and vectorial Hamiltonian maps for systems in dimension smaller than or equal to 4 are given.

Key words: Hamiltonian systems, Poisson manifolds, symplectic structures, generalized Hamiltonian dynamics of Nambu.
2000 Mathematics Subject Classification: 53D10, 53D17, 70G45, 70H05.