Hokkaido Mathematical Journal

Quaternionic CR geometry

Hiroyuki KAMADA and Shin NAYATANI

Full-text: Open access

Abstract

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 [4] is also made.

Article information

Source
Hokkaido Math. J., Volume 42, Number 2 (2013), 159-207.

Dates
First available in Project Euclid: 3 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.hokmj/1372859584

Digital Object Identifier
doi:10.14492/hokmj/1372859584

Mathematical Reviews number (MathSciNet)
MR3112455

Zentralblatt MATH identifier
1044.53032

Subjects
Primary: 32V05: CR structures, CR operators, and generalizations
Secondary: 53C15: General geometric structures on manifolds (almost complex, almost product structures, etc.) 53C26: Hyper-Kähler and quaternionic Kähler geometry, "special" geometry

Keywords
hyper CR structure quaternionic CR structure pseudohermitian structure ultra-pseudoconvex canonical connection

Citation

KAMADA, Hiroyuki; NAYATANI, Shin. Quaternionic CR geometry. Hokkaido Math. J. 42 (2013), no. 2, 159--207. doi:10.14492/hokmj/1372859584. https://projecteuclid.org/euclid.hokmj/1372859584


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