Abstract
We investigate the Yamabe constant's behaviour in a conformal Ricci flow. For conformal Ricci flow metric g(t), t is an element of [0, T), the time evolution formula for the Yamabe constant Y (g(t)) is derived. It is demonstrated that if the beginning metric g(0) = g(0) is Yamabe metric, then the Yamabe constant is monotonically growing along the conformal Ricci flow under some simple assumptions unless g(0) is Einstein. As a result, this study adds to the body of knowledge about the Yamabe problem.