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On some family of generalized Einstein metric conditions

Deszcz R., Hotloś M., Senturk Z.

Demonstratio Mathematica

2001

Vol. 34, nr 4

943-954

We prove that every Einstein manifold of dimension > 4 satisfies some pseudosymmetry type curvature condition. Basing on this fact we introduce a family of curvature conditions. We investigate non-Einstein manifolds satisfying one of these conditions. We prove that every such manifold is pseudosymmetric and satisfies other curvature conditions. We prove also an inverse theorem.