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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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https://hal.archives-ouvertes.fr/hal-00807496
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Submitted on : Wednesday, April 3, 2013 - 4:25:29 PM
Last modification on : Saturday, January 15, 2022 - 4:14:35 AM
Long-term archiving on: : Sunday, April 2, 2017 - 11:44:18 PM

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  • HAL Id : hal-00807496, version 1

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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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