Dirac flow on the 3-sphere (Q530290)

The author defines and studies the Dirac flow: \({\frac {\partial g}{\partial t}=\sqrt{\mathrm{Ric}(g)-4Kg}}\), where \(g\) is a metric conformally equivalent to the round metric on the sphere \(S^3\); this flow describes metrics of constant curvature. Also this flow is studied in the case when \(g(t)\) depends on two functional parameters. Moreover the flow on \(\mathbb{R}P^3\) which gives the Eguchi-Hanson metric is defined by \({\frac {{\partial g}_{ij}}{\partial t}}={1\over 2}{\sqrt{\det(\mathrm{Ric})}({\mathrm{Ric}^{-1})_{ij}}}\), where \(i,j \in \{1,2,3\}\). Finally, singularities developed by these flows are studied in some cases.