On 3-dimensional CR manifolds and twistors

Olivier Biquard[1]

  • [1] Université Louis Pasteur et CNRS IRMA 7 rue René Descartes 67084 Strasbourg cedex (France)

Annales de l’institut Fourier (2007)

  • Volume: 57, Issue: 4, page 1161-1180
  • ISSN: 0373-0956

Abstract

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We prove that any real analytic strictly pseudoconvex CR 3-manifold is the boundary (at infinity) of a unique selfdual Einstein metric defined in a neighborhood. The proof uses a new construction of twistor space based on singular rational curves.

How to cite

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Biquard, Olivier. "Sur les variétés CR de dimension 3 et les twisteurs." Annales de l’institut Fourier 57.4 (2007): 1161-1180. <http://eudml.org/doc/10254>.

@article{Biquard2007,
abstract = {Nous montrons qu’une variété CR strictement pseudoconvexe, de dimension 3, analytique réelle, est le bord à l’infini d’une unique métrique d’Einstein autoduale, définie dans un petit voisinage. La preuve s’appuie sur une construction nouvelle d’espaces de twisteurs à l’aide de courbes rationnelles singulières.},
affiliation = {Université Louis Pasteur et CNRS IRMA 7 rue René Descartes 67084 Strasbourg cedex (France)},
author = {Biquard, Olivier},
journal = {Annales de l’institut Fourier},
keywords = {Twistors; selfdual metric; CR manifold},
language = {fre},
number = {4},
pages = {1161-1180},
publisher = {Association des Annales de l’institut Fourier},
title = {Sur les variétés CR de dimension 3 et les twisteurs},
url = {http://eudml.org/doc/10254},
volume = {57},
year = {2007},
}

TY - JOUR
AU - Biquard, Olivier
TI - Sur les variétés CR de dimension 3 et les twisteurs
JO - Annales de l’institut Fourier
PY - 2007
PB - Association des Annales de l’institut Fourier
VL - 57
IS - 4
SP - 1161
EP - 1180
AB - Nous montrons qu’une variété CR strictement pseudoconvexe, de dimension 3, analytique réelle, est le bord à l’infini d’une unique métrique d’Einstein autoduale, définie dans un petit voisinage. La preuve s’appuie sur une construction nouvelle d’espaces de twisteurs à l’aide de courbes rationnelles singulières.
LA - fre
KW - Twistors; selfdual metric; CR manifold
UR - http://eudml.org/doc/10254
ER -

References

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