[Parallelizable 4-manifolds without complex structure whose twistor space is complex]
The aim of this Note is to give some applications of twistor theory about existence or non-existence of complex structures. We slightly improve Yau's 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.
Le but de cette Note est de donner quelques applications de la théorie des espaces twistoriels à l'existence ou l'inexistence 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 d'une structure complexe. À l'inverse, on explicite une famille de 4-variétés parallélisables sans structure complexe, mais dont le produit avec la sphère est complexe.
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Guillaume Deschamps 1
@article{CRMATH_2005__341_1_35_0, author = {Guillaume Deschamps}, title = {4-vari\'et\'es parall\'elisables sans structure complexe dont l'espace twistoriel est complexe}, journal = {Comptes Rendus. Math\'ematique}, pages = {35--38}, publisher = {Elsevier}, volume = {341}, number = {1}, year = {2005}, doi = {10.1016/j.crma.2005.05.027}, language = {fr}, }
Guillaume Deschamps. 4-variétés parallélisables sans structure complexe dont l'espace twistoriel est complexe. Comptes Rendus. Mathématique, Volume 341 (2005) no. 1, pp. 35-38. doi : 10.1016/j.crma.2005.05.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.05.027/
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