Surfaces in S^3 and H^3 via Spinors

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.

LaTeX, 12 pages

References in corpus (2)

• Eigenvalue estimates for the Dirac-Schrödinger operators
• The energy-momentum tensor as a second fundamental form

Cited by in corpus (7)

• Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds
• Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms
• Spinor representation of Lorentzian surfaces in R^{2,2}
• Spinorial representation of submanifolds in metric Lie groups
• Surfaces in three-dimensional Lie groups in terms of spinors
• Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing Spin${}^c$ spinors
• Characterization of hypersurfaces in four dimensional product spaces via two different Spin${}^c$ structures