Some Results on $*-$Ricci Flow

Abstract

In this paper we have introduced the notion of $*-$ Ricci flow and shown that $*-$ Ricci soliton which was introduced by Kakimakamis and Panagiotid in 2014, is a self similar soliton of the $*-$ Ricci flow. We have also find the deformation of geometric curvature tensors under $*-$ Ricci flow. In the last two section of the paper, we have found the $\Im$-functional and $\omega-$ functional for $*-$ Ricci flow respectively.