Sophus Lie Seminar at UiT

23 Nov 2018 Friday 10:30-12:00, room TEKNO 2.020.

Keegan Flood (University of Auckland)

"Scalar Curvature and Projective Compactification".

In this talk we will use projective tractor calculus to describe the geometry of solutions to the PDE governing the metrizability of projective manifolds. As a consequence we will see that under suitable scalar curvature assumptions the "boundary at infinity" of a projectively compact pseudo-Riemannian metric inherits a well-behaved geometric structure from that of the interior. We will examine the non-vanishing scalar curvature case which yields a conformal structure on boundary, then the scalar-flat case which yields a projective structure on the boundary.