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On left invariant CR structures on $$SU(2)$$. (English) Zbl 1164.32304
Summary: There is a well known one–parameter family of left invariant CR structures on $$SU(2)\cong S^3$$. We show how purely algebraic methods can be used to explicitly compute the canonical Cartan connections associated to these structures and their curvatures. We also obtain explicit descriptions of tractor bundles and tractor connections.

##### MSC:
 32V05 CR structures, CR operators, and generalizations 53B15 Other connections 53C07 Special connections and metrics on vector bundles (Hermite-Einstein, Yang-Mills)
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