Curvature estimates on a parabolic flow of Fei-Guo-Phong

Abstract

In \cite{FGP}, Fei, Guo and Phong established a criteria for the long-time existence of their parabolic flow from $11$-dimensional supergravity, which involves Riemannian curvatures ${\rm Rm}(g(t))$ and 4-forms $F(t)$. In this paper, we obtain a new criteria for the long-time existence of the same flow, which involves only Ricci curvatures ${\rm Ric}(g(t))$, $F(t)$, but as well as $\nabla_{g(t)}F(t)$.