Abstract.
Let x:M→\tilde M be an isometric immersion of a hypersurface M into an (n+1)-dimensional Riemannian manifold \tilde M and let ρ i (i∈{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 ρ i are isoparametric functions and the set (ρ1,...,ρ 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 π=P ♭ of P is symplectic harmonic. If M is compact, then its 2nd Betti number b 2≥1.
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Received: April 7, 1999; in final form: January 7, 2000¶Published online: May 10, 2001
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Mihai, I., Rosca, R. & Verstraelen, L. On a class of Einstein hypersurfaces immersed in a Riemannian manifold. Annali di Matematica 180, 71–79 (2001). https://doi.org/10.1007/s10231-001-8198-x
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DOI: https://doi.org/10.1007/s10231-001-8198-x