Submanifolds with parallel second fundamental form in a generalized Hopf manifold (Q1331660)

Let \(M\) be a submanifold of a generalized Hopf manifold \(\overline {M}\). Suppose the following two conditions are satisfied: (i) \(M\) is tangent to the structure vector fields of \(\overline {M}\), (ii) \(M\) has parallel second fundamental form. The author proves that \(M\) satisfying the above condition is a CR-submanifold of \(\overline {M}\).