Evolutions of $S^3$ and $\mathbb{R}P^3$ that describe Eguchi-Hanson metric and metrics of constant curvature

Abstract: In this work we illustrate some well-known facts about the evolution of $S^3$ under the Ricci flow. The Dirac flow we introduce allows us to describe the 4- dimensional metrics with constant curvature. Another new flow leads to the Eguchi-Hanson metric and can be defined either on metric or on corresponding contact forms.