Sur les variétés CR de dimension 3 et les twisteurs
Annales de l'Institut Fourier, Tome 57 (2007) no. 4, pp. 1161-1180.

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.

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.

DOI : https://doi.org/10.5802/aif.2290
Classification : 53C26,  53C28
Mots clés : twisteurs, métrique autoduale, variété CR
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Biquard, Olivier. Sur les variétés CR de dimension 3 et les twisteurs. Annales de l'Institut Fourier, Tome 57 (2007) no. 4, pp. 1161-1180. doi : 10.5802/aif.2290. http://archive.numdam.org/articles/10.5802/aif.2290/

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