On a class of Einstein hypersurfaces immersed in a Riemannian manifold

Let x : M -> (M) over tilde be an isometric immersion of a hypersurface M into an (n + 1)-dimensional Riemannian manifold (M) over tilde and let rho(i) (i is an element of {1, ..., n}) be the principal curvatures of M. We denote by E and P the distinguished vector field and the curvature vector field of M, respectively, in the sense of [8]. If M is structured by a P-parallel connection [7], then it is Einsteinian. In this case, all the curvature 2-forms are exact and other properties induced by E and P are stated. The principal curvatures rho(i) are isoparametric functions and the set (rho(1), ...,rho(n)) defines an isoparametric system [10]. In the last section, we assume that, in addition, M is endowed with an almost symplectic structure. Then, the dual 1- form pi = P-b of P is symplectic harmonic. If M is compact, then its 2nd Betti number b(2) >= 1.