# Isotropic submanifold

From Diffgeom

Template:Symplectic manifold-submanifold property

## Contents

## Definition

A submanifold of a symplectic manifold is termed an **isotropic submanifold** if for any point on the submanifold, the tangent space to the submanifold is an isotropic subspace of the tangent space to the whole manifold, with respect to the symplectic form. By isotropic subspace we mean that the restriction of the symplectic form to the subspace is the zero map.