Dégénerescence locale des transformations conformes pseudo-riemanniennes

Frances, Charles

doi:10.5802/aif.2732

Frances, Charles ¹

¹ Université Paris-Sud Laboratoire de Mathématiques, 91405 ORSAY Cedex.

Annales de l'Institut Fourier, Tome 62 (2012) no. 5, pp. 1627-1669.

Résumé
Abstract

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.

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.

EuDML MR Zbl | 1 citation dans Numdam

DOI : 10.5802/aif.2732

Classification : 53A30, 53C50
Mot clés : transformations conformes, structures pseudo-riemanniennes.
Keywords: conformal maps, pseudo-Riemannian structures.

Affiliations des auteurs :

Frances, Charles ¹

¹ Université Paris-Sud Laboratoire de Mathématiques, 91405 ORSAY Cedex.

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     title = {D\'eg\'enerescence locale des transformations conformes pseudo-riemanniennes},
     journal = {Annales de l'Institut Fourier},
     pages = {1627--1669},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {62},
     number = {5},
     year = {2012},
     doi = {10.5802/aif.2732},
     zbl = {1261.53052},
     mrnumber = {3025150},
     language = {fr},
     url = {http://www.numdam.org/articles/10.5802/aif.2732/}
}

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 Frances, Charles. Dégénerescence locale des transformations conformes pseudo-riemanniennes. Annales de l'Institut Fourier, Tome 62 (2012) no. 5, pp. 1627-1669. doi : 10.5802/aif.2732. http://www.numdam.org/articles/10.5802/aif.2732/

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