Conformally flat kähler spaces

Lesechko, O.; Latysh, O.; Spychak, T.

doi:10.1063/5.0034024

Cited by 8 publications

(3 citation statements)

References 11 publications

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“…A necessary and sufficient condition for a pseudo-Riemannian space to be defined as a conformal flat space is his compliance to the following conditions [3,13] R hijk = P hk g ij´Phj g ik + P ij g hk´Pik g hj , (5.1)…”

Section: Semi-reducible Conformal Flat Spacesmentioning

confidence: 99%

Special semi-reducible pseudo-Riemannian spaces

Федченко

Lesechko

2021

PIGC

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The paper contains necessary conditions allowing to reduce matrix tensors of pseudo-Riemannian spaces to special forms called semi-reducible, under assumption that the tensor defining tensor characteristic of semireducibility spaces, is idempotent. The tensor characteristic is reduced to the spaces of constant curvature, Ricci-symmetric spaces and conformally flat pseudo-Riemannian spaces. The obtained results can be applied for construction of examples of spaces belonging to special types of pseudo-Riemannian spaces. The research is carried out locally in tensor shape, without limitations imposed on a sign of a metric.

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Section: Semi-reducible Conformal Flat Spacesmentioning

confidence: 99%

Special semi-reducible pseudo-Riemannian spaces

Федченко

Lesechko

2021

PIGC

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Section: Introductionmentioning

confidence: 99%

“…The study of the possibility of special pseudo-Riemannian spaces to admit a Kähler structure is one of the main research topics in this theory. Therefore, it does not lose its relevance [6,19].Many authors have studied pseudo-Riemannian spaces with restrictions imposed on internal objects and the metric tensor itself [3,17]. In the theory of Kähler spaces, there are analogues of tensors that play a certain role in the theory of pseudo-Riemannian spaces.…”

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confidence: 99%

Conformal recurrent Kӓhler spaces

Savchenko,

Shevchenko,

Hedulian

2024

PIGC

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In this paper we study pseudo-Riemannian spaces with recurrent tensor of conformal curvature, which admit a Kähler structure. It is proved that Kähler conformally recurrent spaces other than recurrent spaces do not exist, if their dimension is four. Recurrent Kähler spaces are divided into two types. For each type, the internal necessary characteristic is given. Some properties of four-dimensional Kähler conformally recurrent Kähler spaces are studied.

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