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

Dmitri Alekseevsky; Yoshinobu Kamishima

Open Mathematics (2004)

- Volume: 2, Issue: 5, page 732-753
- ISSN: 2391-5455

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topDmitri Alekseevsky, and Yoshinobu Kamishima. "Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds." Open Mathematics 2.5 (2004): 732-753. <http://eudml.org/doc/268728>.

@article{DmitriAlekseevsky2004,

abstract = {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.},

author = {Dmitri Alekseevsky, Yoshinobu Kamishima},

journal = {Open Mathematics},

keywords = {53C55; 57S25},

language = {eng},

number = {5},

pages = {732-753},

title = {Quaternionic and para-quaternionic CR structure on (4n+3)-dimensional manifolds},

url = {http://eudml.org/doc/268728},

volume = {2},

year = {2004},

}

TY - JOUR

AU - Dmitri Alekseevsky

AU - Yoshinobu Kamishima

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

JO - Open Mathematics

PY - 2004

VL - 2

IS - 5

SP - 732

EP - 753

AB - 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.

LA - eng

KW - 53C55; 57S25

UR - http://eudml.org/doc/268728

ER -

## References

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