Evolution of some geometric quantities along the Cotton flow

Abstract

In this paper we have addressed the behaviour of Yamabe constant along the Cotton flow. We have also studied the evolution of ADM mass along the Cotton flow and it is shown that the ADM mass is conserved along the Cotton flow. Among others evolution of Bach tensor under Cotton flow is derived. It is shown that if the metric of a local conformally flat $3$-manifold evolves under the Cotton flow, then the Bach tensor satisfies the heat equation.