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Curvature properties of Cartan hypersurfaces. (English) Zbl 0816.53032
The notion of semisymmetric Riemannian spaces was introduced by Z. I. Szabo in 1983. This concept was generalized to that of pseudosymmetry and Ricci-pseudosymmetry by R. Deszsz in 1987 and 1989, respectively. Since then several authors have studied the relationship among these notions as well as looked for examples within those families of spaces. For instance, every semisymmetric space is pseudosymmetric and this is in turn Ricci-pseudosymmetric. Converses are not true (we refer the reader to the introduction of the paper for details). In this paper, the authors prove the Cartan hypersurfaces in $$S^{n+1}(c)$$ are examples of non- semisymmetric pseudosymmetric spaces for $$n = 3$$, and of non- pseudosymmetric Ricci-pseudosymmetric manifolds for $$n = 6, 12, 24$$. They also prove other pseudosymmetry type conditions for Cartan hypersurfaces.
Reviewer: O.J.Garay (Bilbao)

##### MSC:
 53C40 Global submanifolds 53C35 Differential geometry of symmetric spaces
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