Paires de structures de contact sur les vari\'et\'es de dimension trois

Abstract

We introduce a notion of positive pair of contact structures on a 3-manifold which generalizes a previous definition of Eliashberg-Thurston and Mitsumatsu. Such a pair gives rise to a locally integrable plane field $\lambda$. We prove that if $\lambda$ is uniquely integrable and if both structures of the pair are tight, then the integral foliation of $\lambda$ doesn't contain any Reeb component whose core curve is homologous to zero. Moreover, the ambient manifold carries a Reebless foliation. We also show a stability theorem "\`a la Reeb" for positive pairs of tight contact structures.