Spinorial characterizations of surfaces into 3-dimensional pseudo-Riemannian space forms

DOI10.1007/s11040-011-9093-3zbMath1242.53019arXiv1001.4198OpenAlexW2051585344WikidataQ115381815 ScholiaQ115381815MaRDI QIDQ430050

Julien Roth, Marie-Amélie Lawn

Publication date: 20 June 2012

Published in: Mathematical Physics, Analysis and Geometry (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1001.4198

zbMATH Keywords

Dirac operatorisometric immersionsKilling spinorsGauss and Codazzi equations

Mathematics Subject Classification ID

Spin and Spin({}^c) geometry (53C27) Local submanifolds (53B25) Local differential geometry of Lorentz metrics, indefinite metrics (53B30)

Related Items (13)

Immersion in \(\mathbb {R}^n\) by complex spinors ⋮ Complex and Lagrangian surfaces of the complex projective plane via Kählerian Killing \(\mathrm{Spin}^c\) spinors ⋮ Spinorial representation of submanifolds in Riemannian space forms ⋮ On the spinorial representation of spacelike surfaces into 4-dimensional Minkowski space ⋮ Spinorial representation of submanifolds in \(\mathrm{SL}_n(\mathbb{C})/\mathrm{SU}(n)\) ⋮ Skew Killing spinors ⋮ Spinorial representation of surfaces into 4-dimensional space forms ⋮ Spinor representation of Lorentzian surfaces in \(\mathbb R^{2, 2}\) ⋮ Spinorial representation of submanifolds in metric Lie groups ⋮ Isometric immersions of hypersurfaces in 4-dimensional manifolds via spinors ⋮ Immersion in \(\mathbb{S}^n\) by complex spinors ⋮ Characterization of hypersurfaces in four-dimensional product spaces via two different \(\text{Spin}^{\text{c}}\) structures ⋮ Spinorial representation of surfaces in Lorentzian homogeneous spaces of dimension 3

Cites Work

• Unnamed Item
• Immersions of Lorentzian surfaces in \(\mathbb R^{2,1}\)
• Isometric immersions of hypersurfaces in 4-dimensional manifolds via spinors
• Spinorial characterizations of surfaces into three-dimensional homogeneous manifolds
• On the spinor representation of surfaces in Euclidean \(3\)-space
• Generalized cylinders in semi-Riemannian and spin geometry
• Codazzi spinors and globally hyperbolic manifolds with special holonomy

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