Heisenberg spin chain models and Bäcklund transformations of isotropic curves in ?3

Abstract

In this paper, we introduce a new complex frame to derive Lamb formalism of an isotropic curve in complex 3-space. From this, we prove that the modified generalizations of the Heisenberg spin chain models in terms of the principal normal vector of an isotropic curve are equivalent to some second-order and third-order complex nonlinear partial differential equations. Finally, we construct B & auml;cklund transformation of an isotropic curve as a transformation which maps an isotropic helix to another isotropic helix congruent to the given one.