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Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds

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Alekseevsky D., Kamishima Y.

Open Mathematics

2004

tom 2

nr 5

732-753

We define notion of a quaternionic and para-quaternionic CR structure on a (4n+3)-dimensional manifold M as a triple (ω1,ω2,ω3) of 1-forms such that the corresponding 2-forms satisfy some algebraic relations. We associate with such a structure an Einstein metric on M and establish relations between quaternionic CR structures, contact pseudo-metric 3-structures and pseudo-Sasakian 3-structures. Homogeneous examples of (para)-quaternionic CR manifolds are given and a reduction construction of non homogeneous (para)-quaternionic CR manifolds is described.

Ograniczanie wyników

1 Open Mathematics

1 Alekseevsky D.

1 Kamishima Y.

1 2004

Wyniki wyszukiwania

Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds