Quaternionic CR Geometry

Modelled on a real hypersurface in a quaternionic manifold, we introduce a quaternionic analogue of CR structure, called quaternionic CR structure. We define the strong pseudoconvexity of this structure as well as the notion of quaternionic pseudohermitian structure. Following the construction of th...

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Bibliographic Details
Published inarXiv.org
Main Authors Kamada, Hiroyuki, Shin Nayatani
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 15.02.2013
Subjects
Construction
Hyperspaces
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Summary:Modelled on a real hypersurface in a quaternionic manifold, we introduce a quaternionic analogue of CR structure, called quaternionic CR structure. We define the strong pseudoconvexity of this structure as well as the notion of quaternionic pseudohermitian structure. Following the construction of the Tanaka-Webster connection in complex CR geometry, we construct a canonical connection associated with a quaternionic pseudohermitian structure, when the underlying quaternionic CR structure satisfies the ultra-pseudoconvexity which is stronger than the strong pseudoconvexity. Comparison to Biquard's quaternionic contact structure is also made.
ISSN:2331-8422