On left invariant CR structures on $SU(2)$

Andreas \v Cap

Institut fuer Mathematik, Universitaet Wien, Nordbergstra{\ss}e15, A--1090 Wien, Austria
International Erwin, Schroedinger Institute for Mathematical Physics, Boltzmanngasse 9, A-1090 Wien, Austria


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.

AMSclassification. 32V05, 53B15, 53C07.