Natural transformations of symplectic structures into Poisson's and Jacobi's brackets

Jacek Debecki

Address. Uniwersytet Jagiellonski, Instytut Matematyki, ul. Reymonta 4, 30-059 Krakow, POLAND,

E-mail: debecki@im.uj.edu.pl

Abstract. A complete classification of natural transformations of symplectic structures into Poisson's brackets as well as into Jacobi's brackets is given.

AMSclassification. 53A55, 53C15

Keywords. Natural operator, symplectic manifold, Poisson manifold, Jacobi manifold