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Comptes Rendus Mathématique
Volume 341, n° 1
pages 35-38 (juillet 2005)
Doi : 10.1016/j.crma.2005.05.027
Received : 12 Mars 2005 ;  accepted : 22 May 2005
4-variétés parallélisables sans structure complexe dont lʼespace twistoriel est complexe
Parallelizable 4-manifolds without complex structure whose twistor space is complex

Guillaume Deschamps
UFR de mathématiques, université Rennes 1, campus de Beaulieu, 35042 Rennes cedex, France 


Le but de cette Note est de donner quelques applications de la théorie des espaces twistoriels à lʼexistence ou lʼinexistence de structures complexes. Ainsi, on précise le résultat de Yau [Topology 15 (1976) 51-53] en donnant la liste complète des 4-variétés réelles compactes parallélisables munies dʼune structure complexe. À lʼinverse, on explicite une famille de 4-variétés parallélisables sans structure complexe, mais dont le produit avec la sphère   est complexe. Pour citer cet article : G. Deschamps, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.

The aim of this Note is to give some applications of twistor theory about existence or non-existence of complex structures. We slightly improve Yauʼs result [Topology 15 (1976) 51-53] by giving the full list of compact parallelizable real 4-manifolds with a complex structure. On the other hand, we give a family of parallelizable 4-manifolds without complex structure but whose product with the sphere   is complex. To cite this article: G. Deschamps, C. R. Acad. Sci. Paris, Ser. I 341 (2005).

The full text of this article is available in PDF format.

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