Maximal tori in contactomorphism groups

Abstract

I describe a general scheme which associates conjugacy classes of tori in the contactomorphism group to transverse almost complex structures on a compact contact manifold. Moreover, to tori of Reeb type whose Lie algebra contains a Reeb vector field one can associate a Sasaki cone. Thus, for contact structures D of K-contact type one obtains a configuration of Sasaki cones called a bouquet such that each Sasaki cone is associated with a conjugacy class of tori of Reeb type.