Contact hypersurfaces of Kähler manifolds
The author classifies contact hypersurfaces \(M\) of Kähler manifolds \(\overline M\) with second fundamental form being a Codazzi tensor. In arbitrary Kähler manifolds, such an \(M\) is either Sasakian and totally umbilical or locally isometric (up to certain transformation) to the unit tangent bundle of a space of constant curvature \(\neq 1\). If \(\overline M\) is a Calabi-Yau manifold (that is, has Ricci-flat Kähler metric), then \(M\) is either Sasakian and umbilical with unit mean curvature, or flat of dimension 3, or locally isometric to \(\mathbb R^{n-1}\times S^n(4)\), \(n > 2\).
scientific article; zbMATH DE number 2067302