nLab
isotropic submanifold

Contents

Definition

Traditional 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 WW of inner product spacecondition on orthogonal space W W^\perp
isotropic subspaceWW W \subset W^\perp
coisotropic subspaceW WW^\perp \subset W
Lagrangian subspaceW=W W = W^\perp(for symplectic form)
symplectic spaceWW ={0}W \cap W^\perp = \{0\}(for symplectic form)

Revised on March 18, 2013 23:51:22 by Urs Schreiber (89.204.138.142)