On left invariant CR structures on \(SU(2)\). (English) Zbl 1164.32304

Čap, Andreas

Arch. Math., Brno 42, No. 5, 185-195 (2006).

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)

Keywords:

Cartan connection; CR structure; curvature; tractor bundle; tractor connection