Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 44, No. 2, pp. 551-558 (2003)

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On pseudosymmetric para-Kählerian manifolds

Dorota {\L}uczyszyn

Institute of Mathematics, Wroc{\l}aw University of Technology, Wybrze\.ze Wyspia\'nskiego 27, PL-50--370 Wroc{\l}aw, Poland

Abstract: In the present paper, we consider para-Kählerian manifolds satisfying various curvature conditions of the pseudosymmetric type. Let $(M,J,g)$ be a para-Kählerian manifold. We prove the following theorems: The Ricci-pseudosymmetry of $(M,J,g)$ reduces to the Ricci-semisymmetry. The pseudosymmetry as well as the Bochner-pseudosymmetry and the paraholomorphic projective-pseudosymmetry of the manifold $(M,J,g)$ always reduces to the semisymmetry in dimensions $>4$. The paraholomorphic projective-pseudosymmetry reduces to the pseudosymmetry in dimension $4$. Moreover, we establish new examples of para-Kählerian manifolds being Ricci-semisymmetric (in dimensions $\geqslant6$) as well as pseudosymmetric (in dimension $4$) or Bochner-pseudosymmetric (in dimension $4$). We have given examples of semisymmetric para-Kählerian manifolds in [L1] and [L2].

[L1] {\L}uczyszyn, D.: On para-Kählerian manifolds with recurrent paraholomorphic projective curvature. Math. Balkanica {\bf 14} (2000), 167--176.

[L2] {\L}uczyszyn, D.: On Bochner semisymmetric para-Kählerian manifolds. Demonstratio Math. {\bf 4} (2001), 933--942.

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Electronic version published on: 1 Aug 2003. This page was last modified: 4 May 2006.

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