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A spinor description of flat surfaces in R^4

We describe the flat surfaces with flat normal bundle and regular Gauss map immersed in R^4 using spinors and Lorentz numbers. We obtain a new proof of the local structure of these surfaces. We also study the flat tori in the sphere S^3 and obtain a new representation formula. We then deduce new proofs of their global structure, and of the global structure of their Gauss map image.

preprint2013arXivOpen access
Pierre Bayard
math.DG
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Pierre Bayard

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