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The Tanaka-Webster connection for almost \(\mathcal S\)-manifolds and Cartan geometry. (English) Zbl 1114.53022

The paper discusses very interesting relations between the so called \(f\)-structures, CR-geometries, pseudo-Hermitian structures and more. The point of view includes the classical approaches to Cartan geometries and results in explicit information on the so called Webster-Tanaka connections. In particular, a CR-integrable \(S\)-structure is interpreted as a reductive Cartan geometry with a canonical linear connection and several properties of this connection are linked with the related structures.

MSC:

53C10 \(G\)-structures
53C15 General geometric structures on manifolds (almost complex, almost product structures, etc.)
53B05 Linear and affine connections
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