On compact holomorphically pseudosymmetric Kählerian manifolds - Mathematics > Differential GeometryReport as inadecuate




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Abstract: For compact K\-ahlerian manifolds, the holomorphic pseudosymmetry reduces tothe local symmetry if additionally the scalar curvature is constant and thestructure function is non-negative. Similarly, the holomorphicRicci-pseudosymmetry reduces to the Ricci-symmetry under these additionalassumptions. We construct examples of non-compact essentially holomorphicallypseudosymmetric K\-ahlerian manifolds. These examples show that the compactnessassumption cannot be omitted in the above stated theorem.Recently, the first examples of compact, simply connected essentiallyholomorphically pseudosymmetric K\-ahlerian manifolds are discovered by W.Jelonek. In his examples, the structure functions change their signs on themanifold.



Author: Zbigniew Olszak

Source: https://arxiv.org/







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