BooksirmaCollected Volumepp. 559–577

Maximally homogeneous para-CR manifolds of semisimple type

  • Dmitri V. Alekseevsky

    University of Edinburgh, United Kingdom
  • Costantino Medori

    Università di Parma, Italy
  • Adriano Tomassini

    Università degli Studi di Parma, Italy
Maximally homogeneous para-CR manifolds of semisimple type cover
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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.