nLab
isotropic submanifold

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Context

Symplectic geometry

symplectic geometry

higher symplectic geometry

Background

Basic concepts

Classical mechanics and quantization

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 W of inner product spacecondition on orthogonal space W ⊥
isotropic subspaceW⊂W ⊥
coisotropic subspaceW ⊥⊂W
Lagrangian subspaceW=W ⊥(for symplectic form)
symplectic spaceW∩W ⊥={0}(for symplectic form)

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