nLab isotropic submanifold

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Definition

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.