Sur les variétés CR de dimension 3 et les twisteurs  [ On 3-dimensional CR manifolds and twistors ]
Annales de l'Institut Fourier, Volume 57 (2007) no. 4, p. 1161-1180
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.
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.
DOI : https://doi.org/10.5802/aif.2290
Classification:  53C26,  53C28
Keywords: Twistors, selfdual metric, CR manifold
@article{AIF_2007__57_4_1161_0,
     author = {Biquard, Olivier},
     title = {Sur les vari\'et\'es CR de dimension 3 et~les~twisteurs},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {57},
     number = {4},
     year = {2007},
     pages = {1161-1180},
     doi = {10.5802/aif.2290},
     zbl = {1124.53014},
     mrnumber = {2339324},
     language = {fr},
     url = {https://aif.centre-mersenne.org/item/AIF_2007__57_4_1161_0}
}
Biquard, Olivier. Sur les variétés CR de dimension 3 et les twisteurs. Annales de l'Institut Fourier, Volume 57 (2007) no. 4, pp. 1161-1180. doi : 10.5802/aif.2290. https://aif.centre-mersenne.org/item/AIF_2007__57_4_1161_0/

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