Ricci Flow on Modified Riemann Extensions

Abstract

We study the properties of Modified Riemann extensions evolving under Ricci flow. We obtain the necessary and sufficient condition for modified Riemann extension under Ricci flow to stay as modified Riemann extension. We also discuss the properties of the curvature tensors under Ricci flow.

Yamabe flow on modified Riemann extension

“…Using 3.2,3.5 and 3.6 we get This is similar to results with Ricci flow and Dissipative Hypergeometric flow [12].…”