Laplacien hypoelliptique et torsion analytique

We establish analytical properties of the hypoelliptic Laplacian on the cotangent bundle of a Riemannian manifold. We show that it is, in the proper sense, a deformation of the classical Laplacian on X. We give a formula relating the analytic torsion of the hypoelliptic Laplacian to the Ray-Singer analytic torsion of the Laplacian of X. To cite this article: J.-M. Bismut, G. Lebeau, C. R. Acad. Sci. Paris, Ser. I 341 (2005).