# Lectures on the geometry of Poisson manifolds

```@inproceedings{Vaisman1994LecturesOT,
title={Lectures on the geometry of Poisson manifolds},
author={Izu Vaisman},
year={1994}
}```
0 Introduction.- 1 The Poisson bivector and the Schouten-Nijenhuis bracket.- 1.1 The Poisson bivector.- 1.2 The Schouten-Nijenhuis bracket.- 1.3 Coordinate expressions.- 1.4 The Koszul formula and applications.- 1.5 Miscellanea.- 2 The symplectic foliation of a Poisson manifold.- 2.1 General distributions and foliations.- 2.2 Involutivity and integrability.- 2.3 The case of Poisson manifolds.- 3 Examples of Poisson manifolds.- 3.1 Structures on ?n. Lie-Poisson structures.- 3.2 Dirac brackets…
954 Citations
1 Geometry of the k-Tangent Bundle TkM.- 1.1 The Category of k-Accelerations Bundles.- 1.2 Liouville Vector Fields. k-Semisprays.- 1.3 Nonlinear Connections.- 1.4 The Dual Coefficients of a Nonlinear
Let (M, P) be a Poisson manifold. A 2-form w of M such that the Koszul bracket {03C9, 03C9}P = 0 is called a complementary form of P. Every complementary form yields a new Lie algebroid structure of
As is well-known, Poisson cohomology is of special importance in the theory of Poisson geometry. But unfortunately, the computation is very complicated because of the lack of a powerful method. Let
• Mathematics
• 2004
2 Poisson geometry and some generalizations 3 2.1 Poisson manifolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Dirac structures . . . . . . . . . . . . . . . . . .
• Mathematics
• 2017
Abstract A cohomology theory associated to a holomorphic Poisson structure is the hypercohomology of a bicomplex where one of the two operators is the classical მ̄-operator, while the other operator
• Mathematics
• 2017
We classify real Poisson structures on complex toric manifolds of type \$(1,1)\$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily
This is a survey exposition of the results of (14) on the relationship between the geometric quantization of a Poisson manifold, of its symplectic leaves and its symplectic realizations, and of the
• Mathematics
• 2014
Motivated by generalized geometry, we discuss differential geometric structures on the total space TMof the bundle TM ⊕ T ∗M , where M is a differentiable manifold; TM is called a big-tangent
• Mathematics
• 2001
Preface. 1. The geometry of tangent bundle. 2. Finsler spaces. 3. Lagrange spaces. 4. The geometry of cotangent bundle. 5. Hamilton spaces. 6. Cartan spaces. 7. The duality between Lagrange and
• Mathematics
• 2022
The paper starts with an interpretation of the complete lift of a Poisson structure from a manifold M to its tangent bundle TM by means of the Schouten-Nijenhuis bracket of covariant symmetric tensor