examples of Lagrangian submanifolds

1. Suppose $M$ is a manifold, and $f:M\to ℝ$ is a smooth function. Then

   $$\{(df)(x)\in T_x^{\ast }(M):x\in M\}$$

   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
Canonical name	ExamplesOfLagrangianSubmanifolds
Date of creation	2013-03-22 15:18:02
Last modified on	2013-03-22 15:18:02
Owner	matte (1858)
Last modified by	matte (1858)
Numerical id	6
Author	matte (1858)
Entry type	Example
Classification	msc 53D05