Classification of almost contact structures associated with a strongly pseudo-convex CR-structure (Q2726122)

Let \(M\) be an orientable \((2n+1)\)-dimensional differentiable manifold. It is well known that a strongly pseudoconvex CR-structure of hypersurface type on \(M\), say \(H(M)\), defines an almost contact structure on \(M\), which is said to be associated to \(H(M)\) [\textit{N. Tanaka}, ``A differential geometric study on strongly pseudoconvex manifolds'', Lect. Math., Kyoto Univ. Vol. 9, Tokyo (1975; Zbl 0331.53025)]. The authors classify the almost contact metric structures associated to strongly pseudoconvex CR-structures of hypersurface type. They apply the results by \textit{D. Chinea} and \textit{C. Gonzalez} [Ann. Mat. Pura Appl. (4) 156, 15-36 (1990; Zbl 0711.53028)], where all almost contact metric structures are classified into 12 different classes. In particular, properties for the gauge transformations under which it is possible to obtain different types of almost contact metric structures associated with the same CR-structure are found. The obtained results are discussed on the unit tangent bundle of a Riemannian manifold of constant sectional curvature and on the Heisenberg Lie group.