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arxiv: 1210.7386 · v1 · pith:EAMS735Rnew · submitted 2012-10-28 · 🧮 math.DG

Spinorial Representation of Surfaces into 4-dimensional Space Forms

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keywords representationsurfacesspacespinorialformsformulaobtaincases
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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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