On Pseudo-Einstein Real Hypersurfaces

Original · EN

Let M be a real hypersurface of a complex space form Mⁿ(c), c≠0, n≥ 3. We show that the Ricci tensor S of M satisfies S(X,Y)=ag(X,Y) for any vector fields X and Y on the holomorphic distribution, a being a constant, if and only if M is a pseudo-Einstein real hypersurface.