Non locally trivializable CR line bundles over compact Lorentzian CR manifolds
[Fibrés en droites CR non localement triviaux sur des variétés CR Lorentziennes compactes]
Brinkschulte, Judith1 ; Hill, C. Denson2
1 Universität Leipzig Mathematisches Institut Augustusplatz 10 D-04109 Leipzig (Germany)
2 Stony Brook University Department of Mathematics Stony Brook NY 11794 (USA)
Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 101-108.

On considère une variété CR compacte de codimension CR quelconque qui vérifie certaines conditions géométriques en terme de sa forme de Levi. Sur ces variétés CR compactes, on construit une déformation du fibré en droites CR trivial sur M qui est topologiquement trivial sur M mais qui n’admet même pas de trivialization CR locale sur un ouvert arbitraire de M. En particulier, nos résultats s’appliquent au cas de variétés CR compactes Lorentziennes du type hypersurface.

We consider compact CR manifolds of arbitrary CR codimension that satisfy certain geometric conditions in terms of their Levi form. Over these compact CR manifolds, we construct a deformation of the trivial CR line bundle over M which is topologically trivial over M but fails to be even locally CR trivializable over any open subset of M. In particular, our results apply to compact Lorentzian CR manifolds of hypersurface type.

Reçu le :
Accepté le :
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DOI : 10.5802/aif.3152
Classification : 32V05, 32G07
Keywords: CR vector bundles, local frames, Lorentzian CR manifolds
Mot clés : fibrés vectoriel CR, repère local, variétés CR Lorentziennes
Brinkschulte, Judith 1 ; Hill, C. Denson 2

1 Universität Leipzig Mathematisches Institut Augustusplatz 10 D-04109 Leipzig (Germany)
2 Stony Brook University Department of Mathematics Stony Brook NY 11794 (USA) 
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     title = {Non locally trivializable $CR$ line bundles over compact {Lorentzian} $CR$ manifolds},
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Brinkschulte, Judith; Hill, C. Denson. Non locally trivializable $CR$ line bundles over compact Lorentzian $CR$ manifolds. Annales de l'Institut Fourier, Tome 68 (2018) no. 1, pp. 101-108. doi : 10.5802/aif.3152. https://www.numdam.org/articles/10.5802/aif.3152/

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