We define the notion of a (weak) almost para-CR structure on a manifold M as a distribution HM ⊂ TM together with a field K ∈ (End(HM)) of involutive endomorphisms of HM. If K satisfies integrability conditions, then (HM, K) is called a (weak) para-CR structure. Under some regularity conditions, an almost para-CR structure can be identified with a Tanaka structure. The notion of maximally homogeneous almost para-CR structure of a semisimple type is defined. A classification of such maximally homogeneous almost para-CR structures is given in terms of appropriate gradations of real semisimple Lie algebras. All such maximally homogeneous structures of depth two (which correspond to depth two gradations) are listed and the integrability conditions are verified.

Maximally homogeneous para-CR manifolds / D. V., Alekseevsky; Medori, Costantino; Tomassini, Adriano. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 30:(2006), pp. 1-27. [10.1007/s10455-005-9009-1]

Maximally homogeneous para-CR manifolds

MEDORI, Costantino;TOMASSINI, Adriano
2006

Abstract

We define the notion of a (weak) almost para-CR structure on a manifold M as a distribution HM ⊂ TM together with a field K ∈ (End(HM)) of involutive endomorphisms of HM. If K satisfies integrability conditions, then (HM, K) is called a (weak) para-CR structure. Under some regularity conditions, an almost para-CR structure can be identified with a Tanaka structure. The notion of maximally homogeneous almost para-CR structure of a semisimple type is defined. A classification of such maximally homogeneous almost para-CR structures is given in terms of appropriate gradations of real semisimple Lie algebras. All such maximally homogeneous structures of depth two (which correspond to depth two gradations) are listed and the integrability conditions are verified.
Maximally homogeneous para-CR manifolds / D. V., Alekseevsky; Medori, Costantino; Tomassini, Adriano. - In: ANNALS OF GLOBAL ANALYSIS AND GEOMETRY. - ISSN 0232-704X. - 30:(2006), pp. 1-27. [10.1007/s10455-005-9009-1]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11381/1505124
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