Generalized Weierstrass representation for surfaces in terms of   Dirac-Hestenes spinor field
  A representation of generalized Weierstrass formulae for an immersion of generic surfaces into a 4-dimensional complex space in terms of spinors treated as minimal left ideals of Clifford algebras is proposed. The relation between integrable deformations of surfaces via mVN-hierarchy and integrable deformations of spinor fields on the surface is also discussed. 
Vadim V. Varlamov