Real hypersurfaces in nonflat complex space forms are irreducible (Q1866573)

The authors prove a fundamental general property of real hypersurfaces; namely, there do not exist real hypersurfaces which are Riemannian products of Riemannian manifolds, both in the complex projective spaces and in the complex hyperbolic spaces. It should be recalled that real projective spaces and real hyperbolic spaces admit ample hypersurfaces which are the Riemannian products of some Riemannian manifolds.