Ricci Flow of Compact Locally Homogeneous Geometries on 5Manifolds
Amanda Hirschmann, Thomas Bell,
2017.08.02
http://arxiv.org/abs/1708.00869
This project serves to analyze the behavior of Ricci Flow in five dimensional
manifolds. Ricci Flow was introduced by Richard Hamilton in 1982 and was an
essential tool in proving the Geometrization and Poincare Conjectures. In
general, Ricci Flow is a nonlinear PDE whose solutions are rather difficult to
calculate; however, in a homogeneous manifold, the Ricci Flow reduces to an
ODE. The behavior of Ricci Flow in two, three, and four dimensional homogenous
manifolds has been calculated and is well understood. The work presented here
will describe efforts to better understand the behavior of Ricci Flow in a
certain class of five dimensional homogeneous manifolds.
