scholarly journals Poly-symplectic Groupoids and Poly-Poisson Structures

2015 ◽  
Vol 105 (5) ◽  
pp. 693-721 ◽  
Author(s):  
Nicolas Martinez
Keyword(s):  
Poisson Structures ◽  
Symplectic Groupoids

scholarly journals Hyperkähler metrics near Lagrangian submanifolds and symplectic groupoids

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Maxence Mayrand
Keyword(s):  
Symplectic Manifold ◽  
Cotangent Bundle ◽  
Lagrangian Submanifolds ◽  
Poisson Manifold ◽  
Lagrangian Submanifold ◽  
Zero Section ◽  
Poisson Structures ◽  
Symplectic Structures ◽  
Symplectic Groupoids ◽  
Hyperkähler Metrics

Abstract The first part of this paper is a generalization of the Feix–Kaledin theorem on the existence of a hyperkähler metric on a neighborhood of the zero section of the cotangent bundle of a Kähler manifold. We show that the problem of constructing a hyperkähler structure on a neighborhood of a complex Lagrangian submanifold in a holomorphic symplectic manifold reduces to the existence of certain deformations of holomorphic symplectic structures. The Feix–Kaledin structure is recovered from the twisted cotangent bundle. We then show that every holomorphic symplectic groupoid over a compact holomorphic Poisson surface of Kähler type has a hyperkähler structure on a neighborhood of its identity section. More generally, we reduce the existence of a hyperkähler structure on a symplectic realization of a holomorphic Poisson manifold of any dimension to the existence of certain deformations of holomorphic Poisson structures adapted from Hitchin’s unobstructedness theorem.

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

scholarly journals DOUBLE BRUHAT CELLS AND SYMPLECTIC GROUPOIDS

2017 ◽  
Vol 23 (3) ◽  
pp. 765-800 ◽  
Author(s):  
JIANG-HUA LU ◽  
VICTOR MOUQUIN
Keyword(s):  
Bruhat Cells ◽  
Symplectic Groupoids

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

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
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