On differentiable compactifications of the hyperbolic space

Benoit Kloeckner (1)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées

The group of direct isometries of the real n-dimensional hyperbolic space is G=SOo(n,1). This isometric action admits many differentiable compactifications into an action on the closed ball. We prove that all such compactifications are topologically conjugate but not necessarily differentiably conjugate. We give the classifications of real analytic and smooth compactifications.

Mots clés: hyperbolic space; compactification; isometries

Domaines: Géométrie métrique [math.MG]; Géométrie différentielle [math.DG]

Benoit Kloeckner. On differentiable compactifications of the hyperbolic space. Transformation Groups, 2006, 11 (2), pp.185-194. ⟨hal-00005233⟩