  In this work we make use of the Ricci flow equations to show that, by
starting from a general ansatz for the metric, we can construct two kinds of
Lifshitz spaces in which: (a) the critical exponent coincides with the spatial
dimension of the spacetime and therefore adopts discrete values, and (b) the
critical exponent is continuous and arbitrary. These results show that Lifshitz
spaces are exact solutions to the Ricci flow equations. Moreover, we found that
the Ricci flow evolves towards a single fixed point for both cases which
coincides with the flat spacetime.
