Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds

Abstract

We give a spinorial characterization of isometrically immersed surfaces into 3-dimensional homogeneous manifolds with 4-dimensional isometry group in terms of the existence of a particular spinor, called generalized Killing spinor. This generalizes results by T. Friedrich for ${\mathbb{R}}^3$ and B. Morel for $\Ss^3$ and $\HH^3$. The main argument is the interpretation of the energy-momentum tensor of a genralized Killing spinor as the second fondamental form up to a tensor depending on the structure of the ambient space

35 pages

References in corpus (2)

• Generalized Cylinders in Semi-Riemannian and Spin Geometry
• Surfaces in S^3 and H^3 via Spinors

Cited by in corpus (12)

• Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms
• On the spinorial representation of spacelike surfaces into 4-dimensional Minkowski space
• Spinorial Representation of Submanifolds in 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
• A discrete extrinsic and intrinsic Dirac operator
• Hypersurfaces of Spin${}^c$ manifolds and Lawson type correspondence
• Spinorial representation of surfaces in Lorentzian homogeneous spaces of dimension 3
• Characterization of hypersurfaces in four dimensional product spaces via two different Spin${}^c$ structures
• The Energy-Momentum tensor on low dimensional $\Spinc$ manifolds