Spinorial Representation of Surfaces into 4-dimensional Space Forms
  In this paper we give a geometrically invariant spinorial representation of surfaces in four-dimensional space forms. In the Euclidean space, we obtain a representation formula which generalizes the Weierstrass representation formula of minimal surfaces. We also obtain as particular cases the spinorial characterizations of surfaces in $\R^3$ and in $S^3$ given by T. Friedrich and by B. Morel 
Pierre Bayard, Marie-Amelie Lawn, Julien Roth
math.DG