Projective Structures and Mobility on 30th January 2013 in Canberra
It has been known for at least 2,500 years that different
Riemannian metrics can have the same geodesics (as unparameterised curves).
However, this phenomenon is quite rare: the generic metric has little
"mobility." More generally, one could try to fit a metric to a system of
curves that one would like to be its geodesics but generically this is
hopeless: no "mobility" at all! I'll explain some of this classical area
(Beltrami 1865, Liouville 1889) from a modern perspective (tractor bundles
and the like).
My notes for the talk
Projective symmetries A follow-up
exposition of the PDE controlling the infinitesimal symmetries of a