Spinorial representation of surfaces in four-dimensional Space Forms

Abstract : 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.
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Pierre Bayard, Marie-Amélie Lawn, Julien Roth. Spinorial representation of surfaces in four-dimensional Space Forms. Annals of Global Analysis and Geometry, Springer Verlag, 2013, 44 (4), pp.433-453. ⟨hal-00807496⟩

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