  Degenerate submanifolds of pseudo-Riemannian manifolds are quite difficult to
study because there is no prefered connection when the submanifold is not
totally geodesic. For the particular case of degenerate totally umbilical
hypersurfaces, we show that there are "Weyl" connections adapted to the induced
structure on the hypersurface. We begin the study of these with their holonomy.
