Maximally homogeneous para-CR manifolds of semisimple type

Abstract

An almost para-CR structure on a manifold M is given by a distribution HM ⊂ TM together with a field K ∈ (End(HM)) of involutive endomorphisms of HM. If K satisfies an integrability condition, then (HM,K) is called a para-CR structure. The notion of maximally homogeneous para-CR structure of a semisimple type is given. A classification of such maximally homogeneous para-CR structures is given in terms of appropriate gradations of real semisimple Lie algebras.