Parallel pure spinors and holonomy

Aziz Ikemakhen

doi:10.1016/S1631-073X(03)00275-9

Geometry

Parallel pure spinors and holonomy
[Spineurs purs parallèles et holonomie]

Présenté par : Étienne Ghys

Aziz Ikemakhen ¹

¹ Faculté des sciences et techniques, BP 549, Guéliz, Marrakech, Morocco

Comptes Rendus. Mathématique, Volume 337 (2003) no. 3, pp. 179-184.

Résumé
Abstract

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 : 2003-03-11
Accepté le : 2003-05-24
Publié le : 2003-07-12

DOI : 10.1016/S1631-073X(03)00275-9

Affiliations des auteurs :

Aziz Ikemakhen ¹

¹ Faculté des sciences et techniques, BP 549, Guéliz, Marrakech, Morocco

@article{CRMATH_2003__337_3_179_0,
     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},
}

TY  - JOUR
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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(03)00275-9/

Bibliographie
Cité par

[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

Cité par Sources :

Commentaires - Politique