Integrable Isotropic Geometrical Flows and Heisenberg Ferromagnets

Geometrical flows (GF) play an important role in modern mathematics and physics. In this letter we have considered some integrable isotropic GF – Ricci flows (RF) and mean curvature flows (MCF) – which are related with integrable Heisenberg ferromagnets. In 2+1 dimensions, these GF have a singularity at $t=t_0$.