We study Sobolev estimates for the solutions of parabolic equations acting on a vector bundle, in a complete, compact or non compact, riemannian manifold . The idea is to introduce geometric weights on . We get global Sobolev estimates with these weights. As applications, we find and improve « classical results », i.e. results without weights, by use of a Theorem by Hebey and Herzlich. As an example we get Sobolev estimates for the solutions of the heat equation on -forms when the manifold has « weak bounded geometry » of order .
