Maciej Dunajski

University of Cambridge (Cambridge, UK)

A problem of Roger Liouville

Abstract:
Cover a plane with curves, one curve through each point in each direction. How can you tell whether these curves are the geodesics of some metric? This problem gives rise to a certain closed system of partial differential equations and hence to obstructions to finding such a metric. It has been an open problem for at least 120 years. I shall present a twistor inspired solution obtained jointly with Robert Bryant and Mike Eastwood.