A mechanics for the Ricci flow
  We construct the classical mechanics associated with a conformally flat Riemannian metric on a compact, n-dimensional manifold without boundary. The corresponding gradient Ricci flow equation turns out to equal the time-dependent Hamilton-Jacobi equation of the mechanics so defined. 
S. Abraham, P. Fernandez de Cordoba, J.M. Isidro, J.L.G. Santander