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Surfaces in 𝕊 3 and 3 via spinors

Bertrand Morel (2004/2005)

Séminaire de théorie spectrale et géométrie

We generalize the spinorial characterization of isometric immersions of surfaces in 3 given by T. Friedrich to surfaces in 𝕊 3 and 3 . The main argument is the interpretation of the energy-momentum tensor associated with a special spinor field as a second fundamental form. It turns out that such a characterization of isometric immersions in terms of a special section of the spinor bundle also holds in the case of hypersurfaces in the Euclidean 4 -space.

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