Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 44, No. 2, pp. 551558 (2003) 

On pseudosymmetric paraKählerian manifoldsDorota {\L}uczyszynInstitute of Mathematics, Wroc{\l}aw University of Technology, Wybrze\.ze Wyspia\'nskiego 27, PL50370 Wroc{\l}aw, PolandAbstract: In the present paper, we consider paraKählerian manifolds satisfying various curvature conditions of the pseudosymmetric type. Let $(M,J,g)$ be a paraKählerian manifold. We prove the following theorems: The Riccipseudosymmetry of $(M,J,g)$ reduces to the Riccisemisymmetry. The pseudosymmetry as well as the Bochnerpseudosymmetry and the paraholomorphic projectivepseudosymmetry of the manifold $(M,J,g)$ always reduces to the semisymmetry in dimensions $>4$. The paraholomorphic projectivepseudosymmetry reduces to the pseudosymmetry in dimension $4$. Moreover, we establish new examples of paraKählerian manifolds being Riccisemisymmetric (in dimensions $\geqslant6$) as well as pseudosymmetric (in dimension $4$) or Bochnerpseudosymmetric (in dimension $4$). We have given examples of semisymmetric paraKählerian manifolds in [L1] and [L2]. [L1] {\L}uczyszyn, D.: On paraKählerian manifolds with recurrent paraholomorphic projective curvature. Math. Balkanica {\bf 14} (2000), 167176. [L2] {\L}uczyszyn, D.: On Bochner semisymmetric paraKählerian manifolds. Demonstratio Math. {\bf 4} (2001), 933942. Full text of the article:
Electronic version published on: 1 Aug 2003. This page was last modified: 4 May 2006.
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