Riemannian metrics on projectively flat manifolds
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.