Real hypersurfaces in complex space forms which are warped products

It is proved in [6] that there do not exist real hypersurfaces in nonflat complex space forms which are Riemannian products of Riemannian manifolds. By contrast, using Legendre curves we construct in this article many examples of real hypersurfaces in complex space forms which are warped products of Riemannian manifolds. Conversely, we prove that our examples are the only real hypersurfaces in complex space forms which are warped products of a complex hypersurface and a curve.