A spinor description of flat surfaces in R4
Abstract
We describe the flat surfaces with flat normal bundle and regular Gauss map immersed in R4 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 S3 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.
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