Skew Killing spinors

Georges Habib; Julien Roth

Open Mathematics (2012)

  • Volume: 10, Issue: 3, page 844-856
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Georges Habib, and Julien Roth. "Skew Killing spinors." Open Mathematics 10.3 (2012): 844-856. <http://eudml.org/doc/269135>.

@article{GeorgesHabib2012,
abstract = {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.},
author = {Georges Habib, Julien Roth},
journal = {Open Mathematics},
keywords = {Spin structures; Isometric immersions; Symmetric Codazzi tensor; Conformally flat; spin structures; isometric immersions; symmetric Codazzi tensor; conformally flat},
language = {eng},
number = {3},
pages = {844-856},
title = {Skew Killing spinors},
url = {http://eudml.org/doc/269135},
volume = {10},
year = {2012},
}

TY - JOUR
AU - Georges Habib
AU - Julien Roth
TI - Skew Killing spinors
JO - Open Mathematics
PY - 2012
VL - 10
IS - 3
SP - 844
EP - 856
AB - 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.
LA - eng
KW - Spin structures; Isometric immersions; Symmetric Codazzi tensor; Conformally flat; spin structures; isometric immersions; symmetric Codazzi tensor; conformally flat
UR - http://eudml.org/doc/269135
ER -

References

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  9. [9] Kusner R., Schmitt N., The spinor representation of surfaces in space, preprint available at http://arxiv.org/abs/dgga/9610005 
  10. [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 Zbl1242.53019
  11. [11] Morel B., Surfaces in 𝕊 3 and ℍ 3 via spinors, In: Semin. Theor. Spectr. Geom., 23, Univ. Grenoble I, Institut Fourier, Saint-Martin-d’Hères, 2005, 131–144 Zbl1106.53004
  12. [12] O’Neill B., Semi-Riemannian Geometry, Pure Appl. Math., 103, Academic Press, New York-London, 1983 
  13. [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 Zbl0688.53007

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