Surfaces in 𝕊 3 and ℍ 3 via spinors
Séminaire de théorie spectrale et géométrie, Tome 23 (2004-2005), pp. 131-144

We generalize the spinorial characterization of isometric immersions of surfaces in ℝ 3 given by T. Friedrich to surfaces in 𝕊 3 and ℍ 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.

DOI : 10.5802/tsg.235
Classification : 53C27, 53C45, 53A10
Keywords: spin geometry, surface, energy-momentum tensor 
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     author = {Bertrand Morel},
     title = {Surfaces in $\mathbb{S}^3$ and $\mathbb{H}^3$ via spinors},
     journal = {S\'eminaire de th\'eorie spectrale et g\'eom\'etrie},
     pages = {131--144},
     year = {2004-2005},
     publisher = {Institut Fourier},
     address = {Grenoble},
     volume = {23},
     doi = {10.5802/tsg.235},
     mrnumber = {2270227},
     zbl = {1106.53004},
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Bertrand Morel. Surfaces in $\mathbb{S}^3$ and $\mathbb{H}^3$ via spinors. Séminaire de théorie spectrale et géométrie, Tome 23 (2004-2005), pp. 131-144. doi: 10.5802/tsg.235

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