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. | ||
Revision as of 11:13, 31 August 2007
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.