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Geometry of Poisson Structures
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Z. Giunashvili
Published/Copyright:
February 23, 2010
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.
Key words and phrases.: Poisson structure; Schoten bracket, bivector field; degenerate Poisson bracket; cohomology of Poisson structure
Received: 1993-10-21
Published Online: 2010-02-23
Published in Print: 1995-August
© 1995 Plenum Publishing Corporation
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Keywords for this article
Poisson structure;
Schoten bracket, bivector field;
degenerate Poisson bracket;
cohomology of Poisson structure
Articles in the same Issue
- On Optimal Stopping of Inhomogeneous Standard Markov Processes
- Geometry of Poisson Structures
- Necessary and Sufficient Conditions for Weighted Orlicz Class Inequalities for Maximal Functions and Singular Integrals. I
- On the Solvability of A Spatial Problem of Darboux Type for the Wave Equation
- On Proper Oscillatory and Vanishing at Infinity Solutions of Differential Equations with A Deviating Argument
- Global Dimensions of Subidealizer Rings
- Regular Fréchet–Lie Groups of Invertible Elements in Some Inverse Limits of Unital Involutive Banach Algebras
