Geometry of Poisson structures
Copyright policy )Geometry of Poisson structures
Abstract The purpose of this paper is to consider certain mechanisms of the emergence of Poisson structures on a manifold. We shall also establish some properties of the bivector field that defines a Poisson structure and investigate geometrical structures on the manifold induced by such fields. Further, we shall touch upon the dualism between bivector fields and differential 2-forms.
- Georgian Technical University Georgia
Poisson structures, Infinite-dimensional Lie groups and their Lie algebras: general properties, KAKS bracket, General geometric structures on manifolds (almost complex, almost product structures, etc.), Kostant-Arnold-Kirillov-Souriau structure, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Groups acting on specific manifolds, Schouten bracket
Poisson structures, Infinite-dimensional Lie groups and their Lie algebras: general properties, KAKS bracket, General geometric structures on manifolds (almost complex, almost product structures, etc.), Kostant-Arnold-Kirillov-Souriau structure, Dynamical aspects of finite-dimensional Hamiltonian and Lagrangian systems, Groups acting on specific manifolds, Schouten bracket
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