On compact holomorphically pseudosymmetric Kählerian manifolds

Details On compact holomorphically pseudosymmetric Kählerian manifolds On compact holomorphically pseudosymmetric Kählerian manifolds

2009-03-29

arxiv.org/abs/0903.5078v2

Cent. Eur. J. Math. 7(3) (2009), 442-451

Mathematics

Differential Geometry

Scientific paper

10.2478/s11533-009-0023-6

For compact K\"ahlerian 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 K\"ahlerian 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 K\"ahlerian manifolds are discovered by W. Jelonek. In his examples, the structure functions change their signs on the manifold.

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