2/11/2005

Kengo Hirachi
University of Tokyo and Princeton University

Fefferman-Graham's ambient metric construction beyond the obstruction

In 1985, Fefferman and Graham introduced a method of constructing conformal invariants of n-dimensional manifolds by using a Ricci-flat, Lorentzian manifold of dimension n+2, which is now called the ambient space. This construction works perfectly well when n is odd, but it is obstructed at a finite jet when n is even. In this talk, I will describe a way to get over this obstruction by considering a Ricci-flat metric with singularity. In particular, I will formulate a jet isomorphism theorem in even-dimensional conformal geometry. (This is an interim report on a joint work with Robin Graham.)