# Maximally homogeneous para-CR manifolds of semisimple type - Mathematics > Differential Geometry

Abstract: An almost para-CR structure on a manifold $M$ is given by a distribution $HM\subset TM$ together with a field $K \in \Gamma{ m End}HM$ of involutiveendomorphisms of $HM$. If $K$ satisfies an integrability condition, then$HM,K$ is called a para-CR structure. The notion of maximally homogeneouspara-CR structure of a semisimple type is given. A classification of suchmaximally homogeneous para-CR structures is given in terms of appropriategradations of real semisimple Lie algebras.

Author: Dmitri V. Alekseevsky, Costantino Medori, Adriano Tomassini

Source: https://arxiv.org/