On the extension of the Harmonic Ricci flow

In this short paper, we prove that if the Ricci curvature is uniformly bounded under the Harmonic Ricci flow on complete manifolds for time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${t\in [0,T)}$$\end{document}, then the Harmonic Ricci flow can be extended past the time T.