A geometric flow based in the Riemann-Christoffel curvature tensor that in two dimensions has some common features with the usual Ricci flow is presented. For n dimensional spaces this new flow takes into account all the components of the intrinsic curvature. For four dimensional Lorentzian manifolds it is found that the solutions of the Einstein equations associated to a 'detonant' sphere of matter, as well, as a Friedman-Roberson-Walker cosmological model are examples of Riemann-Christoffel flows. Possible generalizations are mentioned.47513121315