Symplectic submanifold: Difference between revisions

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A [[submanifold]] of a [[symplectic manifold]] (viz a [[differential manifold]] with a symplectic structure) is termed a '''symplectic submanifold''' if the symplectic form on the manifold, induces, by restriction, a symplectic form on the submanifold. With this symplectic form obtained by restriction, the submanifold becomes a symplectic manifold in its own right.
A [[submanifold]] of a [[symplectic manifold]] (viz a [[differential manifold]] with a symplectic structure) is termed a '''symplectic submanifold''' if the symplectic form on the manifold, induces, by restriction, a symplectic form on the submanifold. With this symplectic form obtained by restriction, the submanifold becomes a symplectic manifold in its own right.
==Relation with other properties==
===Stronger properties===
* [[Isotropic submanifold]]
* [[Coisotropic submanifold]]
* [[Lagrangian submanifold]]

Latest revision as of 20:10, 18 May 2008

Definition

Symbol-free definition

A submanifold of a symplectic manifold (viz a differential manifold with a symplectic structure) is termed a symplectic submanifold if the symplectic form on the manifold, induces, by restriction, a symplectic form on the submanifold. With this symplectic form obtained by restriction, the submanifold becomes a symplectic manifold in its own right.