isotropic submanifold

A submanifold of a symplectic manifold each tangent space of which is an isotropic subspace with respect to the ambient symplectic structure is an **isotropic submanifold**.

type of subspace $W$ of inner product space | condition on orthogonal space $W^\perp$ | |
---|---|---|

isotropic subspace | $W \subset W^\perp$ | |

coisotropic subspace | $W^\perp \subset W$ | |

Lagrangian subspace | $W = W^\perp$ | (for symplectic form) |

symplectic space | $W \cap W^\perp = \{0\}$ | (for symplectic form) |

Last revised on March 18, 2013 at 23:51:22. See the history of this page for a list of all contributions to it.