Non locally trivializable $CR$ line bundles over compact Lorentzian $CR$ manifolds

Judith Brinkschulte; C. Denson Hill

Non locally trivializable $CR$ line bundles over compact Lorentzian $CR$ manifolds

Complex Variables 2019-05-29 v1

Authors: Judith Brinkschulte , C. Denson Hill

Abstract

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.

Keywords

CR line bundles Lorentzian CR manifolds Levi form locally trivializable hypersurface type

Cite

@article{arxiv.1706.05346,
  title  = {Non locally trivializable $CR$ line bundles over compact Lorentzian $CR$ manifolds},
  author = {Judith Brinkschulte and C. Denson Hill},
  journal= {arXiv preprint arXiv:1706.05346},
  year   = {2019}
}

Comments

to appear in Annales de l'Institut Fourier

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