Comptes Rendus
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.

Published online:
DOI: 10.1016/S1631-073X(03)00275-9
Aziz Ikemakhen 1

1 Faculté des sciences et techniques, BP 549, Guéliz, Marrakech, Morocco
     author = {Aziz Ikemakhen},
     title = {Parallel pure spinors and holonomy},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {179--184},
     publisher = {Elsevier},
     volume = {337},
     number = {3},
     year = {2003},
     doi = {10.1016/S1631-073X(03)00275-9},
     language = {en},
AU  - Aziz Ikemakhen
TI  - Parallel pure spinors and holonomy
JO  - Comptes Rendus. Mathématique
PY  - 2003
SP  - 179
EP  - 184
VL  - 337
IS  - 3
PB  - Elsevier
DO  - 10.1016/S1631-073X(03)00275-9
LA  - en
ID  - CRMATH_2003__337_3_179_0
ER  - 
%0 Journal Article
%A Aziz Ikemakhen
%T Parallel pure spinors and holonomy
%J Comptes Rendus. Mathématique
%D 2003
%P 179-184
%V 337
%N 3
%I Elsevier
%R 10.1016/S1631-073X(03)00275-9
%G en
%F CRMATH_2003__337_3_179_0
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.

[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

Cited by Sources:

Comments - Policy

Articles of potential interest

Groupes d'holonomie et spineurs parallèles sur les variétés pseudo-riemanniennes complètement réductibles

Aziz Ikemakhen

C. R. Math (2004)

Eigenvalue estimates for the Dirac operator and harmonic 1-forms of constant length

Andrei Moroianu; Liviu Ornea

C. R. Math (2004)

Supersymmetric backgrounds from generalized Calabi–Yau manifolds

Mariana Graña; Ruben Minasian; Michela Petrini; ...

C. R. Phys (2004)