[Fibrés en droites non localement triviaux sur des variétés Lorentziennes compactes]
On considère une variété compacte de codimension quelconque qui vérifie certaines conditions géométriques en terme de sa forme de Levi. Sur ces variétés compactes, on construit une déformation du fibré en droites trivial sur qui est topologiquement trivial sur mais qui n’admet même pas de trivialization locale sur un ouvert arbitraire de . En particulier, nos résultats s’appliquent au cas de variétés compactes Lorentziennes du type hypersurface.
We consider compact manifolds of arbitrary codimension that satisfy certain geometric conditions in terms of their Levi form. Over these compact manifolds, we construct a deformation of the trivial line bundle over which is topologically trivial over but fails to be even locally trivializable over any open subset of . In particular, our results apply to compact Lorentzian manifolds of hypersurface type.
Accepté le :
Publié le :
Keywords: $CR$ vector bundles, local frames, Lorentzian $CR$ manifolds
Mot clés : fibrés vectoriel $CR$, repère local, variétés $CR$ Lorentziennes
@article{AIF_2018__68_1_101_0,
author = {Brinkschulte, Judith and Hill, C. Denson},
title = {Non locally trivializable $CR$ line bundles over compact {Lorentzian} $CR$ manifolds},
journal = {Annales de l'Institut Fourier},
pages = {101--108},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
volume = {68},
number = {1},
year = {2018},
doi = {10.5802/aif.3152},
language = {en},
url = {http://archive.numdam.org/articles/10.5802/aif.3152/}
}
TY - JOUR AU - Brinkschulte, Judith AU - Hill, C. Denson TI - Non locally trivializable $CR$ line bundles over compact Lorentzian $CR$ manifolds JO - Annales de l'Institut Fourier PY - 2018 SP - 101 EP - 108 VL - 68 IS - 1 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.3152/ DO - 10.5802/aif.3152 LA - en ID - AIF_2018__68_1_101_0 ER -
%0 Journal Article %A Brinkschulte, Judith %A Hill, C. Denson %T Non locally trivializable $CR$ line bundles over compact Lorentzian $CR$ manifolds %J Annales de l'Institut Fourier %D 2018 %P 101-108 %V 68 %N 1 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.3152/ %R 10.5802/aif.3152 %G en %F AIF_2018__68_1_101_0
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. http://archive.numdam.org/articles/10.5802/aif.3152/
[1] On the absence of Poincaré lemma in tangential Cauchy-Riemann complexes, Ann. Sc. Norm. Super. Pisa, Cl. Sci., Volume 8 (1981), pp. 365-404 | Zbl
[2] Obstructions to finite dimensional cohomology of abstract Cauchy-Riemann complexes, Ann. Sc. Norm. Super. Pisa, Cl. Sci., Volume 15 (2016), pp. 343-354 | Zbl
[3] On the nonvanishing of abstract Cauchy–Riemann cohomology groups, Math. Ann., Volume 363 (2016) no. 3-4, pp. 1701-1715 | DOI | Zbl
[4] The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, 57, Princeton University Press, 1972, viii+146 pages | Zbl
[5] Counterexamples to Newlander-Nirenberg up to the boundary, Several complex variables and complex geometry (Proceedings of Symposia in Pure Mathematics), Volume 52, American Mathematical Society, 1991, pp. 191-197 | Zbl
[6] Pseudoconcave manifolds, Complex analysis and geometry (Lecture Notes in Pure and Applied Mathematics), Volume 173, Marcel Dekker (1996), pp. 275-297 | Zbl
[7] A weak pseudoconcavity condition for abstract almost manifolds, Invent. Math., Volume 142 (2000) no. 2, pp. 251-283 | DOI | Zbl
[8] The integrability problem for vector bundles, Several complex variables and complex geometry (Proceedings of Symposia in Pure Mathematics), Volume 52, American Mathematical Society, 1991, pp. 355-368 | Zbl
Cité par Sources :
