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[parent] examples of Lagrangian submanifolds (Example)
  1. Suppose $M$ is a manifold, and $ f\colon M\to \mathbbmss{R}$ is a smooth function. Then $$ \{ (df)(x)\in T^\ast _x(M) : x\in M\} $$ is a Lagrangian submanifold of the cotangent bundle $T^\ast M$ when this is equipped with the canonical symplectic structure.



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Cross-references: structure, canonical, cotangent bundle, Lagrangian submanifold, smooth function, manifold

This is version 3 of examples of Lagrangian submanifolds, born on 2005-05-22, modified 2006-09-20.
Object id is 7099, canonical name is ExamplesOfLagrangianSubmanifolds.
Accessed 1562 times total.

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AMS MSC: 53D05 (Differential geometry :: Symplectic geometry, contact geometry :: Symplectic manifolds, general)
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