Yannick Herfray (ULB) will speak in the geometry seminar on Tuesday 29 January, at 1.30pm in the Salle de Profs. Yannick’s title is Conformally invariant geodesics in asymptotically hyperbolic manifolds and his abstract is below.
This talk will be on recent results in conformal geometry that Joel Fine and I obtained. In the first part of the talk I will try to review the main three standard tools in the field in a way that insists on their geometrical unity : tractor calculus, the so-called (n+2-dimensional) Ambient metric of Fefferman and Graham and the associated (n+1-dimensional) Poincaré-Einstein metric, best known for its ubiquity in holographic context.
I will then use these to discuss a natural conformally invariant version of geodesic lines. The tractor calculus description of these “conformal geodesics” has been known for a long time but the holographic (I.e Poincare) and ambient metric realisations are new. Essentially we proved that being a conformal geodesic is one-to-one correspondence with asymptotic vanishing of the extrinsic curvature of a “dual” minimal surface in the PE space.