On Bochner flat para-Kählerian manifolds

Dorota Łuczyszyn

Open Mathematics (2005)

  • Volume: 3, Issue: 2, page 331-341
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Dorota Łuczyszyn. "On Bochner flat para-Kählerian manifolds." Open Mathematics 3.2 (2005): 331-341. <http://eudml.org/doc/268876>.

@article{DorotaŁuczyszyn2005,
abstract = {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.},
author = {Dorota Łuczyszyn},
journal = {Open Mathematics},
keywords = {53C15; 53C50; 53C56},
language = {eng},
number = {2},
pages = {331-341},
title = {On Bochner flat para-Kählerian manifolds},
url = {http://eudml.org/doc/268876},
volume = {3},
year = {2005},
}

TY - JOUR
AU - Dorota Łuczyszyn
TI - On Bochner flat para-Kählerian manifolds
JO - Open Mathematics
PY - 2005
VL - 3
IS - 2
SP - 331
EP - 341
AB - 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.
LA - eng
KW - 53C15; 53C50; 53C56
UR - http://eudml.org/doc/268876
ER -

References

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