Handbook of Pseudo-Riemannian Geometry and Supersymmetry

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pp: 559–577

DOI: 10.4171/079-1/16

Maximally homogeneous para-CR manifolds of semisimple type

Dmitri V. Alekseevsky[1], Costantino Medori[2] and Adriano Tomassini[3]

(1) University of Edinburgh, United Kingdom
(2) Università di Parma, Italy
(3) Università degli Studi di Parma, Italy

An almost para-CR structure on a manifold M is given by a distribution HMTM 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.

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