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.
@article{bwmeta1.element.doi-10_2478_BF02475974,
author = {Dmitri Alekseevsky and Yoshinobu Kamishima},
title = {Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds},
journal = {Open Mathematics},
volume = {2},
year = {2004},
pages = {732-753},
zbl = {1116.53046},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02475974}
}
Dmitri Alekseevsky; Yoshinobu Kamishima. Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds. Open Mathematics, Tome 2 (2004) pp. 732-753. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02475974/
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