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.
@article{bwmeta1.element.doi-10_2478_BF02499218,
author = {Dorota \L uczyszyn},
title = {On Bochner flat para-K\"ahlerian manifolds},
journal = {Open Mathematics},
volume = {3},
year = {2005},
pages = {331-341},
zbl = {1107.53021},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_BF02499218}
}
Dorota Łuczyszyn. On Bochner flat para-Kählerian manifolds. Open Mathematics, Tome 3 (2005) pp. 331-341. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_BF02499218/
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