Dégénerescence locale des transformations conformes pseudo-riemanniennes

Frances, Charles

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

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.

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