Hokkaido Mathematical Journal
- Hokkaido Math. J.
- Volume 42, Number 2 (2013), 159-207.
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 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.
Hokkaido Math. J., Volume 42, Number 2 (2013), 159-207.
First available in Project Euclid: 3 July 2013
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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