Integrable Isotropic Geometrical Flows and Heisenberg Ferromagnets

TL;DR

This paper explores integrable isotropic geometrical flows, specifically Ricci and mean curvature flows, and their connection to Heisenberg ferromagnets, highlighting singularities in 2+1 dimensions.

Contribution

It establishes a link between integrable geometrical flows and Heisenberg ferromagnets, focusing on their behavior and singularities in higher dimensions.

Findings

Identification of singularities at t=t0 in 2+1 dimensions.

Connection between Ricci flows, mean curvature flows, and Heisenberg ferromagnets.

Analysis of integrability in isotropic geometrical flows.

Abstract

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 $t=t_{0}$.