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 \(\mathbb R ^3\) and in \(S^3\) given by Friedrich and by Morel.
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Bayard, P., Lawn, MA. & Roth, J. Spinorial representation of surfaces into 4-dimensional space forms. Ann Glob Anal Geom 44, 433–453 (2013). https://doi.org/10.1007/s10455-013-9375-z
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DOI: https://doi.org/10.1007/s10455-013-9375-z