Abstract

The Blaschke metric is a projectively invariant metric on a strictly convex domain in a flat real projective manifold, which generalizes the Klein model hyperbolic metric. The boundary inherits a geometric structure called conformal Codazzi structure. In this talk, we consider the volume expansion of the Blaschke metric and construct a global conformal invariant of the boundary. We also define the Q-curvature for conformal Codazzi structures, which integrates to that invariant.