Skew Killing spinors

• Autorzy: Georges Habib , Julien Roth
• Języki publikacji: EN

Abstrakty

EN

We study the existence of a skew Killing spinor on 2- and 3-dimensional Riemannian spin manifolds. We establish the integrability conditions and prove that these spinor fields correspond to twistor spinors in the two dimensional case while, up to a conformal change of the metric, they correspond to parallel spinors in the three dimensional case.

Słowa kluczowe

EN

Spin structures; Isometric immersions; Symmetric Codazzi tensor; Conformally flat

Kategorie tematyczne

• 53C80: Applications to physics
• 53C27: Spin and Spin c geometry
• 53C40: Global submanifolds

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2012
• Tom: 10
• Numer: 3
• Strony: 844-856

Daty

wydano

2012-06-01

online

2012-03-24

Twórcy

autor

Georges Habib

• Lebanese University

autor

Julien Roth

• Université Paris-Est Marne-la-Vallée

Bibliografia

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• [9] Kusner R., Schmitt N., The spinor representation of surfaces in space, preprint available at http://arxiv.org/abs/dgga/9610005
• [10] Lawn M.-A., Roth J., Spinorial characterizations of surfaces into 3-dimensional pseudo-Riemannian space forms, Math. Phys. Anal. Geom., 2011, 14(3), 185–195 http://dx.doi.org/10.1007/s11040-011-9093-3
• [11] Morel B., Surfaces in \(\mathbb{S}^3 \) and \(\mathbb{H}^3 \) via spinors, In: Semin. Theor. Spectr. Geom., 23, Univ. Grenoble I, Institut Fourier, Saint-Martin-d’Hères, 2005, 131–144
• [12] O’Neill B., Semi-Riemannian Geometry, Pure Appl. Math., 103, Academic Press, New York-London, 1983
• [13] Wang McK.Y., Parallel spinors and parallel forms, Ann. Global Anal. Geom., 1989, 7(1), 59–68 http://dx.doi.org/10.1007/BF00137402

Identyfikatory

DOI

10.2478/s11533-012-0029-3