Integrable geometric evolution equations through a deformed Heisenberg spin equation

Abstract

Using the geometrical equivalence methods, we showed a deformed Heisenberg spin chain equation is geometrically equivalent to a generalized nonlinear Schrödinger equation. After that, we demonstrate in Euclidean 3-space that assigning spin vectors to the tangent, normal, and binormal vectors of the three distinct moving space curves, respectively, results in the creation of three distinct surfaces. Then we find the Gauss and the mean curvatures of these surfaces, respectively. © 2025 Elsevier B.V.