Comptes Rendus
Geometry
Parallel pure spinors and holonomy
Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 179-184.

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

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.

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Accepted:
Published online:
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/

[1] W. Ambrose; I.M. Singer A theorem on holonomy, Trans. Amer. Math. Soc., Volume 79 (1953), pp. 428-443

[2] H. Baum; I. Kath Parallel spinors and holonomy groups on pseudo-Riemannian spin manifolds, Ann. Glog. Anal. Geom., Volume 17 (1999), pp. 1-17

[3] L. Berard Bergery; A. Ikemakhen On the holonomy of Lorentzian manifolds, Proc. Sympos. Pure Math., 54, 1993, pp. 27-40 (Part 2)

[4] L. Berard Bergery; A. Ikemakhen Sur l'holonomie des variétés pseudo-riemanniennes de signature (n,n), Bull. Soc. Math. France, Volume 125 (1997) no. 1, pp. 93-114

[5] I. Kath; I. Kath Parallel pure spinors on pseudo-Riemannian manifolds (W.H. Chen et al., eds.), Geometry and Topology of Submanifolds X, Proceedings of the Conference on Differential Geometry in Honor of Prof. S.S. Chern, Beijing, China, August 29–September 3Parallel pure spinors on pseudo-Riemannian manifolds, The Workshop on PDEs and Submanifolds, Berlin, Germany, November 26–28, 1999, pp. 87-103

[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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