Séance Séminaire

Séminaire Gaston Darboux

A topological method for Webster curvature prescription

CR manifolds are manifolds endowed with a geometric structure motivated by the study of real hypersurfaces of the complex space. CR manifolds admit a local invariant known as Webster curvature analogous to scalar curvature for Riemannian manifolds, and the problem of finding a conformal change in such a way to make it equal to a given function has been widely studied. In this seminar I will introduce the problem and then describe how to calculate the Leray-Schauder degree of the sets of solutions of the problem in dimension three for a generic class of functions, which gives as a corollary an existence result.