Locally Lagrangian Symplectic and Poisson Manifolds

2000/08/14 by Izu Vaisman, Vaisman, Izu
Mathematics · Physics and Astronomy · #53D05 #53D12 #53D17 #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Nonlinear Waves and Solitons #Symplectic Geometry (math.SG) #math.SG #msc:53D05 #msc:53D12 #msc:53D17

paper · pdf · doi:10.48550/arxiv.math/0008097

LaTex, 21 pages. Lecture at ``Poisson 2000'', CIRM, Luminy, France, June 26-30, 2000

arxiv created 2000/08/14 · openalex publication_date 2000/08/14 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss symplectic manifolds where, locally, the structure is that encountered in Lagrangian dynamics. Exemples and characteristic properties are given. Then, we refer to the computation of the Maslov classes of a Lagrangian submanifold. Finally, we indicate the generalization of this type of structures to Poisson manifolds.

Related

• Deformations of log-Lagrangian submanifolds of Poisson manifolds
• Symplectic Geometry, Poisson Geometry, and Beyond
• Symplectic realizations of holomorphic Poisson manifolds
• Maslov class of lagrangian embedding to Kahler manifold
• On the variety of Lagrangian subalgebras