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On Bochner semisymmetric para-Kahlerian manifolds

Łuczyszyn D.

Demonstratio Mathematica

2001

Vol. 34, nr 4

933-942

A semisymmetric (R'R = 0) para-Kahlerian manifold is obviously Bochner semisymmetric (R' B = 0). In the present paper, we prove the following partially inverse theorem: If a para-Kahlerian manifold is Bochner semisymmetric and the Bochner curvature tensor B does not vanish at each point of the manifold, then the manifold is semisymmetric. Moreover, we establish new examples of para-Kahlerian manifolds which are: (1) semisymmetric and not Bochner flat; (2) Bochner flat and not semisymmetric.