The ambient metric to all orders in even dimensions

Tuesday, July 25, 2006 - 9:00am - 9:45am
EE/CS 3-180
Robin Graham (University of Washington)
The ambient metric associated to a conformal manifold is an
important object in conformal geometry. However, the basic construction
is obstructed at finite order in even dimensions. This talk will describe
how to complete the construction to all orders in even dimensions. One
obtains a family of smooth ambient metrics determined up to smooth
diffeomorphism. These ambient metrics arise as an invariantly defined
smooth part of inhomogeneous Ricci-flat metrics with asymptotic expansions
involving log terms. This is joint work with Kengo Hirachi.