For compact Kählerian manifolds, the holomorphic pseudosymmetry reduces to the local symmetry if additionally the scalar curvature is constant and the structure function is non-negative. Similarly, the holomorphic Ricci-pseudosymmetry reduces to the Ricci-symmetry under these additional assumptions. We construct examples of non-compact essentially holomorphically pseudosymmetric Kählerian manifolds. These examples show that the compactness assumption cannot be omitted in the above stated theorem. Recently, the first examples of compact, simply connected essentially holomorphically pseudosymmetric Kählerian manifolds are discovered in [4]. In these examples, the structure functions change their signs on the manifold.
@article{bwmeta1.element.doi-10_2478_s11533-009-0023-6,
author = {Zbigniew Olszak},
title = {On compact holomorphically pseudosymmetric K\"ahlerian manifolds},
journal = {Open Mathematics},
volume = {7},
year = {2009},
pages = {442-451},
zbl = {1185.53081},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0023-6}
}
Zbigniew Olszak. On compact holomorphically pseudosymmetric Kählerian manifolds. Open Mathematics, Tome 7 (2009) pp. 442-451. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-009-0023-6/
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