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Open Mathematics

formerly Central European Journal of Mathematics

Editor-in-Chief: Gianazza, Ugo / Vespri, Vincenzo

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Volume 3, Issue 2

Issues

Volume 13 (2015)

On Bochner flat para-Kählerian manifolds

Dorota Łuczyszyn
Published Online: 2005-06-01 | DOI: https://doi.org/10.2478/BF02499218

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: Para-Kählerian manifold; Bochner conformal curvature; Bochner flat manifold

Keywords: 53C15; 53C50; 53C56

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About the article

Published Online: 2005-06-01

Published in Print: 2005-06-01


Citation Information: Open Mathematics, Volume 3, Issue 2, Pages 331–341, ISSN (Online) 2391-5455, DOI: https://doi.org/10.2478/BF02499218.

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© 2005 Versita Warsaw. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

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