CUNY Graduate Center Differential Geometry Seminar presents

Riemannian metrics on projectively flat manifolds

John Loftin, Columbia University

Wednesday, February 7

2:30-3:30 pm, Room 4419

The first part of the talk will be a small survey of the differential geometry and geometric PDEs on manifolds with restricted coordinate charts. The motivating example of Kahler-Einstein metrics on complex manifolds will be discussed alongside examples of other ``canonical'' metrics in different geometries. In particular, work of Schoen-Yau in conformally flat geometry and Cheng-Yau in affine flat geometry will be exposed. Then I'll discuss recent work in which I prove that the existence of a certain type of Riemannian metric, roughly analogous to a Kahler metric, on a projectively flat manifold forces the manifold to be a projective quotient of a bounded domain. Finally I'll give more background on this geometry and an idea of the proof.