Cotton flow

Kisisel, Ali Ulas Ozgur; Sarioglu, Ozgur; Tekin, Bayram

Cotton flow

Authors

Kisisel, Ali Ulas Ozgur

Sarioglu, Ozgur

Tekin, Bayram

Description

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. Two of the nine homogeneous geometries, which are degenerated by the Ricci flow, are left intact by the Cotton flow.
17 pages, 4 figures, exact solutions of two geometries given, exposition of several parts expanded, references updated