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A Singularity Theorem for Twistor Spinors

Florin Alexandru Belgun[1]; Nicolas Ginoux[2]; Hans-Bert Rademacher[1]

  • [1] Universität Leipzig Mathematisches Institut Johannisgasse 26 04109 Leipzig (Allemagne)
  • [2] Universität Potsdam Institut für Mathematik - Geometrie Am Neuen Palais 10 14469 Potsdam (Allemagne)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 4, page 1135-1159
  • ISSN: 0373-0956

Abstract

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We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples.

How to cite

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Belgun, Florin Alexandru, Ginoux, Nicolas, and Rademacher, Hans-Bert. "A Singularity Theorem for Twistor Spinors." Annales de l’institut Fourier 57.4 (2007): 1135-1159. <http://eudml.org/doc/10253>.

@article{Belgun2007,
abstract = {We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples.},
affiliation = {Universität Leipzig Mathematisches Institut Johannisgasse 26 04109 Leipzig (Allemagne); Universität Potsdam Institut für Mathematik - Geometrie Am Neuen Palais 10 14469 Potsdam (Allemagne); Universität Leipzig Mathematisches Institut Johannisgasse 26 04109 Leipzig (Allemagne)},
author = {Belgun, Florin Alexandru, Ginoux, Nicolas, Rademacher, Hans-Bert},
journal = {Annales de l’institut Fourier},
keywords = {Orbifolds; twistor-spinors; ALE spaces; orbifolds; ale spaces},
language = {eng},
number = {4},
pages = {1135-1159},
publisher = {Association des Annales de l’institut Fourier},
title = {A Singularity Theorem for Twistor Spinors},
url = {http://eudml.org/doc/10253},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Belgun, Florin Alexandru
AU - Ginoux, Nicolas
AU - Rademacher, Hans-Bert
TI - A Singularity Theorem for Twistor Spinors
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 4
SP - 1135
EP - 1159
AB - We study spin structures on orbifolds. In particular, we show that if the singular set has codimension greater than 2, an orbifold is spin if and only if its smooth part is. On compact orbifolds, we show that any non-trivial twistor spinor admits at most one zero which is singular unless the orbifold is conformally equivalent to a round sphere. We show the sharpness of our results through examples.
LA - eng
KW - Orbifolds; twistor-spinors; ALE spaces; orbifolds; ale spaces
UR - http://eudml.org/doc/10253
ER -

References

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  13. P.B. Kronheimer, The construction of ALE spaces as hyperkähler quotients, J. Diff. Geom. 29 (1989), 665-683 Zbl0671.53045MR992334
  14. W. Kühnel, H.-B. Rademacher, Twistor Spinors and Gravitational Instantons, Lett. Math. Phys. 38 (1996), 411-419 Zbl0860.53029MR1421685
  15. W. Kühnel, H.-B. Rademacher, Conformal completion of U ( n ) –invariant Ricci flat Kähler metrics at infinity, Zeitschr. Anal. Anwend. 16 (1997), 113-117 Zbl0870.53040MR1453395
  16. W. Kühnel, H.-B. Rademacher, Asymptotically Euclidean Manifolds and Twistor Spinors, Commun. Math. Phys. 196 (1998), 67-76 Zbl0929.53023MR1643509
  17. A. Lichnerowicz, Killing spinors, twistor–spinors and Hijazi inequality, J. Geom. Phys. 5 (1988), 2-18 Zbl0678.53018MR1027531
  18. P. Petersen, Riemannian Geometry, 171 (1998), Springer Zbl0914.53001MR1480173
  19. A. Sardo-Infirri, Partial Resolutions of orbifold singularities via moduli spaces of HYM-type bundles 

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