I am trying to my head around these two things in the context of string theory. The Polyakov action becomes simpler to solve in the conformal gauge which, as I understand it, makes the manifold locally Ricci flat in 2D. In Professor Susskind's lectures on String Theory he introduces the concept of Ricci flow (approx minute 35).. Both seem to achieve the same result. Is the difference related to sub-manifold versus background (ambient)?