Generalization of Hasimoto's transformation
  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 \psi introduced by Hasimoto in terms of moving frames associated to a natural complex bundle over the filament. 
Mathieu Molitor
math.DG