Dégénerescence locale des transformations conformes pseudo-riemanniennes  [ Local degeneracy of pseudo-Riemannian conformal transformations ]
Annales de l'Institut Fourier, Volume 62 (2012) no. 5, p. 1627-1669

We study the set Conf(M,N) of conformal immersions between two pseudo-Riemannian manifolds (M,g) and (N,h). We characterize the closure of Conf(M,N) in the space of continuous maps from M to N, and we investigate the geometric properties of (M,g) whenever this closure is nontrivial.

Nous étudions l’ensemble Conf(M,N) des immersions conformes entre deux variétés pseudo-riemanniennes (M,g) et (N,h). Nous caractérisons notamment l’adhérence de Conf(M,N) dans l’espace des applications continues 𝒞 0 (M,N), et décrivons quelques propriétés géométriques de (M,g) lorsque cette adhérence est non triviale.

DOI : https://doi.org/10.5802/aif.2732
Classification:  53A30,  53C50
Keywords: conformal maps, pseudo-Riemannian structures.
@article{AIF_2012__62_5_1627_0,
     author = {Frances, Charles},
     title = {D\'eg\'enerescence locale des transformations conformes pseudo-riemanniennes},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {62},
     number = {5},
     year = {2012},
     pages = {1627-1669},
     doi = {10.5802/aif.2732},
     mrnumber = {3025150},
     zbl = {1261.53052},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_2012__62_5_1627_0}
}
 Frances, Charles. Dégénerescence locale des transformations conformes pseudo-riemanniennes. Annales de l'Institut Fourier, Volume 62 (2012) no. 5, pp. 1627-1669. doi : 10.5802/aif.2732. http://www.numdam.org/item/AIF_2012__62_5_1627_0/

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