Videos

Finite total $Q$-curvature on a locally conformally flat manifold

Presenter
January 15, 2016
Keywords:
  • differential geometry
  • manifolds
  • curvature
  • geodesic flow
  • Q-curvature
  • integral geometry
  • Gaussian curvature
MSC:
  • 53-xx
  • 53Cxx
  • 53C05
  • 53C07
  • 53C15
  • 53C22
  • 53C44
  • 54A20
  • 53C65
Abstract
In this talk, we will discuss locally conformally flat manifolds with finite total curvature. We prove that for such a manifold, the integral of the $Q$-curvature equals an integral multiple of a dimensional constant. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds. It provides further evidence that $Q$-curvature controls geometry as the Gaussian curvature does in two dimension on locally conformally flat manifolds.
Supplementary Materials