On transversely holomorphic flows. I
The paper studies transversely holomorphic one-dimensional orientable foliations on closed connected three-manifolds. Assume that the foliation satisfies a certain rationality condition, for example if \(\dim H^1(M,\mathbb{R})\leq 1\) or if \(H^2(M,{\mathcal O})= 0\), where \(\mathcal O\) is the sheaf of locally constant functions on leaves and transversely holomorphic. Then, the author shows, that the foliation is one of the examples in the following list. (1) Seifert fibrations. (2) Linear foliations on the three-dimensional torus. (3) Strong stable foliations associated to the suspension of hyperbolic diffeomorphisms on the two-dimensional torus. (4) Suspensions of holomorphic automorphisms of the Riemann sphere. (5) Transversely affine foliations on \(S^2\times S^1\). (6) Foliations in \(S^3\) induced by the singularity of holomorphic vector fields in \((\mathbb{C}^2,0)\) which are in the Poincaré domain.
scientific article; zbMATH DE number 980764