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单词 ConormalBundle
释义

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

{(x,λ)|xX,λTi(x)*M,λ(v)=0vTxX}.

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.

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更新时间:2025/5/3 0:48:51