Exterior differential systems
I will review the basic theory of EDS and the Cartan-Kähler theorem, and then we will turn to some more sophisticated examples. For instance, we will see that every Riemannian 3-manifold locally admits orthogonal coordinates.
If there is time, I will briefly explain the notion of the prolongation of and exterior differential system, and the generality of the solutions obtained from the Cartan-Kähler theorem.
