Conformal mappings preserving the curvature of multi-dimensional platforms

Shevchenko, T. I.; Gudyreva, O.; Fedchenko, Ju.

doi:10.1063/5.0033941

Cited by 3 publications

(2 citation statements)

References 17 publications

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“…here δ h k are Kronecker symbols, and R is a scalar curvature of R = R αβ g αβ , see [14,15]. Substitute (3.1) in the integrability conditions of the tensor characteristic of semi-reducible spaces.…”

Section: Semi-reducible Spaces Of Constant Curvaturementioning

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 Spaces Of Constant Curvaturementioning

confidence: 99%

Special semi-reducible pseudo-Riemannian spaces

Федченко

Lesechko

2021

PIGC

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“…In this respect, we can also mention the works of S. Fedishenko [5,6] who studied conformal mappings preserving the Ricci tensor and the scalar curvature, respectively.…”

Section: Introductionmentioning

confidence: 99%

On conformally reducible pseudo-Riemannian spaces

Shevchenko

Спічак

Дойков

2021

PIGC

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The present paper studies the main type of conformal reducible conformally flat spaces. We prove that these spaces are subprojective spaces of Kagan, while Riemann tensor is defined by a vector defining the conformal mapping. This allows to carry out the complete classification of these spaces. The obtained results can be effectively applied in further research in mechanics, geometry, and general theory of relativity. Under certain conditions the obtained equations describe the state of an ideal fluid and represent quasi-Einstein spaces. Research is carried out locally in tensor shape.

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