Belgun, Florin Alexandru Normal CR structures on \(S^3\). (English) Zbl 1044.32027 Math. Z. 244, No. 1, 125-151 (2003). Let \((M,\alpha)\) be a contact manifold of dimension \(2n+1\). \(\alpha\) determines a vector field \(R\), called Reeb vector field, and a contact distribution \(\xi=\text{ker }\alpha\). Given a complex structure \(J:\xi\to \xi\) compatible with \(d\alpha_\xi\) the pair \((J,\xi)\) is called a normal CR structure on \(M\) if \(L_{R\xi }J\equiv 0\) for the Lie derivative. In this paper the author gives the classifications of the normal CR structures on \(S^3\) and their automorphism groups. Combing with results in another paper [Math. Z. 238, No. 3, 441–460 (2001; Zbl 1043.32020)] this completes the classifications of the normal CR structures on compact \(3\)-manifolds. Moreover the author gives a criterion to compare a structure to normal CR structures and shows that the underlying contact structure is unique up to diffeomorphism. Reviewer: Guang-Cun Lu (Beijing) Cited in 8 Documents MSC: 32V05 CR structures, CR operators, and generalizations 53C25 Special Riemannian manifolds (Einstein, Sasakian, etc.) 53D10 Contact manifolds (general theory) 57M50 General geometric structures on low-dimensional manifolds Keywords:normal CR structures; Sasakian structures; contact structures; compact \(3\)-manifolds Citations:Zbl 1043.32020 PDFBibTeX XMLCite \textit{F. A. Belgun}, Math. Z. 244, No. 1, 125--151 (2003; Zbl 1044.32027) Full Text: DOI