Visualizing Ricci flow of manifolds of revolution

Abstract

We present numerical visualizations of Ricci flow of surfaces and three-dimensional manifolds of revolution. Ricci rot is an educational tool that visualizes surfaces of revolution moving under Ricci flow. That these surfaces tend to remain embedded in ℝ3 is what makes direct visualization possible. The numerical lessons gained in developing this tool may be applicable to numerical simulation of Ricci flow of other surfaces. Similarly for simple three-dimensional manifolds like the 3-sphere, with a metric that is invariant under the action of SO(3) with 2-sphere orbits, the metric can be represented by a 2-sphere of revolution, where the distance to the axis of revolution represents the radi..