Flexibility of ideal triangle groups in complex hyperbolic geometry

Elisha Falbel (1, 2) , Pierre-Vincent Koseleff (1, 2)

1 UPMC - Université Pierre et Marie Curie - Paris 6
2 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We show that the Teichmüller space of the ideal triangle group in the automorphism group of complex hyperbolic space contains a real four-dimensional ball. This implies the existence of a four-dimensional family of spherical CR structures on the trivial circle bundle over the sphere minus three points. The proof is an explicit construction of fundamental domains whose boundaries are special hypersurfaces foliated by complex geodesics.

Mots clés: Complex hyperbolic; Triangle group; Discrete group; CR-manifolds

Domaines: Mathématiques [math]

Elisha Falbel, Pierre-Vincent Koseleff. Flexibility of ideal triangle groups in complex hyperbolic geometry. Topology, 2000, 39 (6), pp.1209-1223. ⟨10.1016/S0040-9383(99)00023-3⟩. ⟨hal-01362306⟩