Theorem of Weinstein
In the symplectic geometry , one of the Hamiltonian mechanics developed branch of mathematics , which is set by Weinstein (ger .: Weinstein's neighborhood theorem ) is a theorem , the environment Lagrangian submanifolds in symplectic manifolds describes.
Theorem of Weinstein
Let be a symplectic manifold and a Lagrangian submanifold .
Then there is a neighborhood of that is symplectomorphic to a neighborhood of the zero intersection in .
The cotangent bundle is provided with the canonical symplectic form in the canonical coordinates .
literature
- Alan Weinstein : Symplectic manifolds and their Lagrangian submanifolds. Advances in Math. 6, 329-346 (1971).
- Ana Cannas da Silva : Introduction to symplectic and Hamiltonian geometry. Publicações Matemáticas do IMPA. Rio de Janeiro, 2003. ISBN 85-244-0195-8