On the normalized Ricci flow with scalar curvature converging to constant (Q783756)

This paper shows that the normalized Ricci flow \(g(t)\) on a smooth closed manifold \(M\) existing for all \(t\ge 0\) with scalar curvature converging to constant in \(L^2\) norm (called semi-Einstein) satisfies \(\liminf_{t\rightarrow \infty}\int_M|\mathring r|^2_{g(t)}d\mu_{g(t)}=0\), where \(\mathring r\) is the trace-free part of the Ricci tensor. Using this, topological obstructions to the existence of such a Ricci flow on \(4\)-manifolds are given.