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On Bochner flat para-Kählerian manifolds

100%

Łuczyszyn D.

Open Mathematics

2005

tom 3

nr 2

331-341

Let B be the Bochner curvature tensor of a para-Kählerian manifold. It is proved that if the manifold is Bochner parallel (∇ B = 0), then it is Bochner flat (B = 0) or locally symmetric (∇ R = 0). Moreover, we define the notion of tha paraholomorphic pseudosymmetry of a para-Kählerian manifold. We find necessary and sufficient conditions for a Bochner flat para-Kählerian manifold to be paraholomorphically pseudosymmetric. Especially, in the case when the Ricci operator is diagonalizable, a Bochner flat para-Kählerian manifold is paraholomorphically pseudosymmetric if and only if the Ricci operator has at most two eigenvalues. A class of examples of manifolds of this kind is presented.

On the bochner conformal curvature of Kähler-Norden manifolds

100%

Olszak K.

Open Mathematics

2005

tom 3

nr 2

309-317

Using the one-to-one correspondence between Kähler-Norden and holomorphic Riemannian metrics, important relations between various Riemannian invariants of manifolds endowed with such metrics were established in my previous paper [19]. In the presented paper, we prove that there is a strict relation between the holomorphic Weyl and Bochner conformal curvature tensors and similarly their covariant derivatives are strictly related. Especially, we find necessary and sufficient conditions for the holomorphic Weyl conformal curvature tensor of a Kähler-Norden manifold to be holomorphically recurrent.

Ograniczanie wyników

2 Open Mathematics

1 Olszak K.

1 Łuczyszyn D.

2 2005

Wyniki wyszukiwania

On Bochner flat para-Kählerian manifolds

On the bochner conformal curvature of Kähler-Norden manifolds