reto muller investigated a new geometric flow which consists of a coupled system of the ricci flow on a closed manifold $m$ with the harmonic map flow of a map $\phi$ from $m$ to some closed target closed manifold $n$, given by $\frac{\partial}{\partial t} g = - 2 ric + 2 \alpha \nabla \phi \bigotimes \nabla \phi, \frac{\partial}{\partial t}\phi = \tau_{g}\phi $, where $\alpha$ is a positive coupling constant. this new flow shares many good properties with the ricci flow.