Real hypersurfaces with a special transversal vector field (Q2901177)

For a real hypersurface in \(\mathbb C^{n+1}\) a transversal vector field \(C\) is called \(J\)-tangent if it is tangent after rotation by the complex structure. Conditions are given for the affine normal to be \(J\)-tangent. \textit{V. Cruceanu} [Result. Math. 13, No. 3--4, 224--234 (1988; Zbl 0646.53007)] treated the centro-affine case where \(C\) is the position vector \(f\). He called a hypersurface special if \(C\) is \(J\)-tangent. More generally, in the present paper a hypersurface is called special if there is a vector field \(C\) in the plane of \(f\) and \(Jf\) which is \(J\)-tangent. In this case, an almost contact structure is induced. Conditions are given for this structure to be normal.