Gel'fand-Dorfman theorem and exact cocycle Poisson structures

1995 ◽  
Vol 34 (3) ◽  
pp. 443-452
Author(s):  
K. H. Bhaskara ◽  
John V. Leahy ◽  
K. Rama
Keyword(s):  
Poisson Structures

scholarly journals Applications of Nijenhuis geometry: non-degenerate singular points of Poisson–Nijenhuis structures

2021 ◽  
Author(s):  
Alexey V. Bolsinov ◽  
Andrey Yu. Konyaev ◽  
Vladimir S. Matveev
Keyword(s):  
Singular Points ◽  
Recursion Operator ◽  
Poisson Structures ◽  
Degeneracy Condition ◽  
Compatible Poisson Structures

AbstractWe study and completely describe pairs of compatible Poisson structures near singular points of the recursion operator satisfying natural non-degeneracy condition.

scholarly journals Poisson structures of near-symplectic manifolds and their cohomology

2021 ◽  
Vol 62 (3) ◽  
pp. 033513
Author(s):  
Panagiotis Batakidis ◽  
Ramón Vera
Keyword(s):  
Symplectic Manifolds ◽  
Poisson Structures

Nilpotent Orbits in Simple Lie Algebras and their Transverse Poisson Structures

2008 ◽  
Author(s):  
P. A. Damianou ◽  
H. Sabourin ◽  
P. Vanhaecke ◽  
Rui Loja Fernandes ◽  
Roger Picken
Keyword(s):  
Lie Algebras ◽  
Poisson Structures ◽  
Nilpotent Orbits ◽  
Simple Lie Algebras

Geometry of Poisson Structures

1995 ◽  
Vol 2 (4) ◽  
pp. 347-359
Author(s):  
Z. Giunashvili
Keyword(s):  
Poisson Structure ◽  
Poisson Structures ◽  
Geometrical 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.

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