Generalization of Hasimoto's transformation

Details Generalization of Hasimoto's transformation Generalization of Hasimoto's transformation

2012-04-24

arxiv.org/abs/1204.5324v1

International Journal of Geometric Methods in Modern Physics, Vol. 6 (2009), no. 4, 625--630

Mathematics

Differential Geometry

Scientific paper

10.1142/S0219887812200010

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.

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