conormal bundle

Let X be an immersed submanifold of M, with immersion i:XM. Then as with the normal bundleMathworldPlanetmath, we can pull the cotangent bundleMathworldPlanetmath back to X, forming a bundle i*T*M. This has a canonical pairing with i*TM, essentially by definition. Since TX is a natural subbundle of i*TM, we can consider its annihilatorPlanetmathPlanetmathPlanetmath: the subbundle of i*T*M given by


This subbundle is denoted N*X, and called the conormal bundle of X.

The conormal bundle to any submanifold is a natural Lagrangian submanifold of T*M.

Title conormal bundle
Canonical name ConormalBundle
Date of creation 2013-03-22 13:59:09
Last modified on 2013-03-22 13:59:09
Owner bwebste (988)
Last modified by bwebste (988)
Numerical id 5
Author bwebste (988)
Entry type Definition
Classification msc 58A32