Evolution of geometric constant evolving along extended Ricci flow

Abstract

We investigate the behavior of the lowest geometric constant, [Formula: see text], along the extended Ricci flow such that there exist positive solutions to the following partial differential equation: [Formula: see text] with [Formula: see text], where [Formula: see text] and [Formula: see text] are real constants. We drive the evolution formula for the geometric constant [Formula: see text] along the unnormalized and normalized extended Ricci flow. Moreover, we give some monotonic quantities involving [Formula: see text] along the extended Ricci flow by imposing some geometric conditions.