On some family of generalized Einstein metric conditions

Ryszard Deszcz, Marian Hotloś, Zerrin Sentürk

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9 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)943-954
Number of pages12
JournalDemonstratio Mathematica
Issue number4
Publication statusPublished - Oct 2001

Bibliographical note

Publisher Copyright:
© 2001 Warsaw University. All rights reserved.


  • Einstein manifold
  • Generalized Einstein metric condition.
  • Pseudosymmetry type manifold


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