Normal CR structures on compact 3-manifolds
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- Belgun, F. Math Z (2001) 238: 441. doi:10.1007/s002090100260
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We study normal CR compact manifolds in dimension 3. For a choice of a CR Reeb vector field, we associate a Sasakian metric on them, and we classify those metrics. As a consequence, the underlying manifolds are topologically finite quotients of \(S^3\) or of a non-flat circle bundle over a Riemann surface of positive genus. In the latter case, we prove that their CR automorphisms group is a finite extension of \(S^1\), and we classify the normal CR structures on these manifolds.