405CRS Riemannian Geometry

Preliminaries

Analytic functions

Riemannian metrics, R manifolds, local diffeomorphisms, Every smooth manifold admits a riemannian metric, the space of riemannian metrics on $M$ is infinite dimensional. Whitney embedding theorem (every smooth manifold is diffeomorphic to an embedded submanifold of an Euclidean space), Nash (every riemannian manifold can be embedded into ${\mathbb{R}}^N$ such that $g={\phi }^{\ast }{g}_E$). Product of manifolds, warp products