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Examples of nonsemisymmetric Ricci-semisymmetric hypersurfaces. (English) Zbl 1026.53010
Suppose M n ,g is a semi-Riemannian manifold of dimension n3. M n ,g is said to be semisymmetric if R·R=0, and Ricci-semisymmetric if R·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 n5 are given as well.
MSC:
53B30Lorentz metrics, indefinite metrics
53B25Local submanifolds
53C40Global submanifolds (differential geometry)
53C35Symmetric spaces (differential geometry)
53B50Applications of local differential geometry to physics
53B20Local Riemannian geometry