Alan Pinoy (Stockholm) will speak in the differential geometry seminar at 2pm on 8th January 2024, in the Salle des Profs (9th floor building NO). Alan’s title is “The geometry at infinity of asymptotically locally complex hyperbolic almost Hermitian manifolds” and his abstract is below.
The complex hyperbolic space is the complex counterpart of real hyperbolic geometry, and is the simplest instance of a negatively curved Kähler-Einstein manifold. Similarly to the real case, the Riemannian geometry of the complex hyperbolic space is in one-to-one correspondance with the conformal geometry of its boundary at infinity, which is a strictly pseudoconvex Cauchy-Riemann (CR) structure. This correspondance has proven useful to the study of complex domains as well as that of Kähler manifolds.
In this talk, we consider a complete, non-compact almost Hermitian manifold whose geometry at infinity is locally modelled on that of the complex hyperbolic space. Under purely geometric considerations, we will prove that such a manifold admits a natural compactification at infinity by a strictly pseudoconvex CR structure.