Quaternionic contact structure with integrable complementary distribution

2019/02/23 by Kamishima, Yoshinobu
#51M10 #53C55 #57S25 #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1902.08796

Abstract

We study positive definite quaternionic contact (4n+3)-manifolds (qc-manifold for short). Just like the CR-structure contains the class of Sasaki manifolds, the qc-structure admits a class of 3-Sasaki manifolds with integrable distribution isomorphic to \mathfraksu(2). A big difference concerning the integrable complementary qc-distribution V of the qc-structure from 3-Sasaki structure is the existence of Lie algebra not isomorphic to \mathfraksu(2). We take up non-compact qc-manifolds to find out a salient feature of topology and geometry in case V generates the qc-transformations R³.

Related

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