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June 2013 Quaternionic CR geometry
Hiroyuki KAMADA, Shin NAYATANI
Hokkaido Math. J. 42(2): 159-207 (June 2013). DOI: 10.14492/hokmj/1372859584

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.

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Hiroyuki KAMADA. Shin NAYATANI. "Quaternionic CR geometry." Hokkaido Math. J. 42 (2) 159 - 207, June 2013. https://doi.org/10.14492/hokmj/1372859584

Information

Published: June 2013
First available in Project Euclid: 3 July 2013

zbMATH: 1044.53032
MathSciNet: MR3112455
Digital Object Identifier: 10.14492/hokmj/1372859584

Subjects:
Primary: 32V05
Secondary: 53C15, 53C26

Rights: Copyright © 2013 Hokkaido University, Department of Mathematics

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Vol.42 • No. 2 • June 2013
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