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.