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BY-NC-ND 3.0 license Open Access Published by De Gruyter Open Access June 1, 2005

On Bochner flat para-Kählerian manifolds

  • Dorota Łuczyszyn EMAIL logo
From the journal Open Mathematics

Abstract

Let B be the Bochner curvature tensor of a para-Kählerian manifold. It is proved that if the manifold is Bochner parallel (∇ B = 0), then it is Bochner flat (B = 0) or locally symmetric (∇ R = 0). Moreover, we define the notion of tha paraholomorphic pseudosymmetry of a para-Kählerian manifold. We find necessary and sufficient conditions for a Bochner flat para-Kählerian manifold to be paraholomorphically pseudosymmetric. Especially, in the case when the Ricci operator is diagonalizable, a Bochner flat para-Kählerian manifold is paraholomorphically pseudosymmetric if and only if the Ricci operator has at most two eigenvalues. A class of examples of manifolds of this kind is presented.

Keywords: 53C15; 53C50; 53C56

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Published Online: 2005-6-1
Published in Print: 2005-6-1

© 2005 Versita Warsaw

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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