Surfaces in S^3 and H^3 via Spinors
Differential Geometry
2007-05-23 v2
Abstract
We generalize the spinorial characterization of isometric immersions of surfaces in R^3 given by T. Friedrich (On the spinor representation of surfaces in Euclidean 3-space, J. Geom. Phys. 28 (1998)) 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.
Cite
@article{arxiv.math/0204090,
title = {Surfaces in S^3 and H^3 via Spinors},
author = {Bertrand Morel},
journal= {arXiv preprint arXiv:math/0204090},
year = {2007}
}
Comments
LaTeX, 12 pages