# examples of Lagrangian submanifolds

1. 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.

Title examples of Lagrangian submanifolds ExamplesOfLagrangianSubmanifolds 2013-03-22 15:18:02 2013-03-22 15:18:02 matte (1858) matte (1858) 6 matte (1858) Example msc 53D05