Torsion of tight contact structures

Thanks to ro to sion, an invariant introduced by E. Giroux. we give a suffi cient topological condition for a 3-manifold to carry infinitely many non-i somorphic tight contact structures. It is for example the case of every orientable Seifert fibered space over a surface of genus g greater than or equal to 1. We also prove a rigidity result for the existence of some contact submanifo lds in a universally tight contact 3-manifold. (C) 2001 Editions scientifiq ues et medicales Elsevier SAS.