Generalization of Hasimoto's transformation

Abstract

In this paper, we generalize the famous Hasimoto's transformation by showing that the dynamics of a closed unidimensional vortex filament embedded in a three-dimensional manifold of constant curvature gives rise under Hasimoto's transformation to the non-linear Schrodinger equation. We also give a natural interpretation of the function ψintroduced by Hasimoto in terms of moving frames associated to a natural complex bundle over the filament.