Comptes Rendus
Geometry
Parallel pure spinors and holonomy
[Spineurs purs parallèles et holonomie]
Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 179-184.

Nous caractérisons les variétés pseudo-riemanniennes spinorielles qui admettent des spineurs purs parallèles par leurs groupes d'holonomie. En particulier, nous étudions le cas des variétés lorentziennes.

We characterize the spin pseudo-Riemannian manifolds which admit parallel pure spinors by their holonomy groups. In particular, we study the Lorentzian case.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(03)00275-9

Aziz Ikemakhen 1

1 Faculté des sciences et techniques, BP 549, Guéliz, Marrakech, Morocco
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Aziz Ikemakhen. Parallel pure spinors and holonomy. Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 179-184. doi : 10.1016/S1631-073X(03)00275-9. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00275-9/

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[6] Th. Leistner Lorentzian manifolds with special holonomy and parallel spinors, in: Proceedings of the 21st Winter School “Geometry and Physics”, Srni, January 13–20, (2001) (Rend. Circ. Mat. Palermo (2) Suppl.), Volume 69 (2002), pp. 131-159

[7] H.B. Lawson; M.-L. Michelsohn Spin Geometry, Princeton University Press, 1989

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