https://neckpinch.com/authors/thomas-bell/New arXiv papers by Thomas Bell, from Neckpinch Tue, 10 Nov 2026 04:10:28 GMT https://neckpinch.com/papers/1708.00869/arxiv:1708.00869Wed, 02 Aug 2017 00:00:00 GMTAmanda Hirschmann, Thomas Bell — 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.Ricci flowPoincaré conjectureGeometrization4-manifoldsHomogeneous spaces