Charles Frances

The conformal boundary of Margulis space–times

Abstract In this Note, we show how to construct the conformal boundary of Margulis space–times R 1,2 /Γ when Γ is an affine Schottky group. To cite this article: C. Frances, C. R. Acad. Sci. Paris, Ser. I 336 (2003).

Local dynamics of conformal vector fields

We study pseudo-Riemannian conformal vector fields in the neighborhood of a singularity. For Riemannian manifolds, we prove that if a conformal vector field vanishing at a point x0 is not Killing for a metric in the conformal class, then a neighborhood of the singularity x0 is conformally flat.

Conformal actions of nilpotent groups on pseudo-Riemannian manifolds

We study conformal actions of connected nilpotent Lie groups on compact pseudo-Riemannian manifolds. We prove that if a type-(p, q) compact manifold M supports a conformal action of a connected nilpotent group H , then the degree of nilpotence of H is at most 2p + 1, assuming p ≤ q; further, if this maximal degree is attained, then M is conformally equivalent to the universal type-(p, q), compact, conformally flat space, up to finite or cyclic covers. The proofs make use of the canonical Cartan geometry associated to a pseudo-Riemannian conformal structure.

Actions of semisimple Lie groups preserving a degenerate Riemannian metric

We prove a rigidity of the lightcone in Minkowski space. It is (essentially) the unique space endowed with a lightlike metric and supporting an isometric nonproper action of a semisimple Lie group.

Removable and essential singular sets for higher dimensional conformal maps

In this article, we prove several results about the extension to the boundary of conformal immersions from an open subset

Lorentzian Kleinian groups

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An Embedding Theorem for Automorphism Groups of Cartan Geometries

of a Riemannian manifold

Sur le groupe d'automorphismes des géométries paraboliques de rang 1

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Formes normales pour les champs conformes pseudo-riemanniens

, into another Riemannian manifold

Causal conformal vector fields, and singularities of twistor spinors

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