Hokkaido Mathematical Journal

KAMADA Hiroyuki, NAYATANI Shin,

Quaternionic CR geometry.

Hokkaido Mathematical Journal, 42 (2013) pp.159-207

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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.

MSC(Primary)32V05
MSC(Secondary)53C15, 53C26
Uncontrolled Keywordshyper CR structure, quaternionic CR structure, pseudohermitian structure, ultra-pseudoconvex, canonical connection