21 Jun 2018; Dept Math & Stat (UiT), room U7=A152. Thursday 13:00-14:00

David Calderbank (University of Bath)

"Subriemannian metrics and metrizability of parabolic geometries"

A classical question in differential geometry is whether the (unparameterized) geodesics of a torsion-free affine connection are also geodesic for a metric. Remarkably, this problem linearizes as an overdetermined first order system for the inverse metric.

In this talk, based on joint work with Jan Slovak and Vladimir Soucek, I will describe a generalization of the above metrizability problem to a large class of geometries called parabolic geometries, and discuss the classification of those geometries for which a similar linearization of the problem is possible. In this generalization, the metrics are typically subriemannian, rather than riemannian, and linearizable example include metrics on free distributions and on generic rank two distributions in five dimensions.