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Examples of nonsemisymmetric Ricci-semisymmetric hypersurfaces. (English) Zbl 1026.53010
Suppose $\left( M^n,g\right)$ is a semi-Riemannian manifold of dimension $n\geq 3$. $\left( M^n,g\right)$ is said to be semisymmetric if $R\cdot R=0$, and Ricci-semisymmetric if $R\cdot S=0$, where $R$ is the Riemann-Christoffel curvature tensor and $S$ is the Ricci tensor on the manifold. In general the first condition implies the second, but not conversely. In this paper the authors construct a class of Ricci-semisymmetric warped products which are not semisymmetric. Examples of Ricci-semisymmetric, non-semisymmetric hypersurfaces in semi-Euclidean space $E_s^{n+1}$ for $n\geq 5$ are given as well.

53B30Lorentz metrics, indefinite metrics
53B25Local submanifolds
53C40Global submanifolds (differential geometry)
53C35Symmetric spaces (differential geometry)
53B50Applications of local differential geometry to physics
53B20Local Riemannian geometry
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