Hamilton-Ivey estimates for the Ricci-Bourguignon flow with $\rho<0$

Abstract

In this paper, we prove Hamilton-Ivey estimates for the Ricci-Bourguignon flow on a compact manifold, with $n=3$ and $\rho<0$. As a consequence, we prove that compact ancient solutions have nonnegative sectional curvature for all negative $\rho$.