On Bochner semisymmetric para-Kählerian manifolds (Q2777567)

Starting with the fact that a semisymmetric (\(R\cdot R=0\)) para-Kählerian manifold is Bochner semisymmetric (\(R\cdot B=0\)), the author proves a partial inverse theorem: If a para-Kählerian manifold \(M\) is Bochner semisymmetric and the Bochner curvature tensor \(B\) does not vanish at each points \(x\in M\), then \(M\) is semisymmetric. Moreover, the author provides examples of para-Kählerian manifolds which are: (1) semisymmetric and not Bochner flat; (2) Bochner flat and not semisymmetric.