Spinorial Characterizations of Surfaces into 3-dimensional pseudo-Riemannian Space Forms

Abstract

We give a spinorial characterization of isometrically immersed surfaces of arbitrary signature into 3-dimensional pseudo-Riemannian space forms. For Lorentzian surfaces, this generalizes a recent work of the first author in ${\mathbb{R}}^{2,1}$ to other Lorentzian space forms. We also characterize immersions of Riemannian surfaces in these spaces. From this we can deduce analogous results for timelike immersions of Lorentzian surfaces in space forms of corresponding signature, as well as for spacelike and timelike immersions of surfaces of signature (0,2), hence achieving a complete spinorial description for this class of pseudo-Riemannian immersions.

9 pages

References in corpus (3)

• Generalized Cylinders in Semi-Riemannian and Spin Geometry
• Spinorial Characterization of Surfaces into 3-dimensional homogeneous Manifolds
• Surfaces in S^3 and H^3 via Spinors

Cited by in corpus (11)

• 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
• A generalized Weierstrass representation of Lorentzian surfaces in ${\mathbb{R}}^{2,2}$ and applications
• Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing Spin${}^c$ spinors
• Skew Killing spinors
• Immersion in Sn by complex spinors
• Immersion in Rn by Complex irreducible Spinors
• Spinorial representation of surfaces in Lorentzian homogeneous spaces of dimension 3
• Immersion in ${\mathbb{R}}^n$ by complex spinors