Cotton flow

Understand

Using the conformally invariant Cotton tensor, we define a geometric flow, the "Cotton flow", which is exclusive to three dimensions.

• This flow tends to evolve the initial metrics into conformally flat ones, and is somewhat orthogonal to the Yamabe flow, the latter being a flow within a conformal class.
• We define an entropy functional, and study the flow of nine homogeneous spaces both numerically and analytically.
• In particular, we show that the arbitrarily deformed homogeneous 3-sphere flows into the round 3-sphere.