Models of mechanical systems preserving the Weyl tensor

Lesechko, O.; Latysh, O.; Kamienieva, A.

doi:10.1063/1.5130794

Cited by 11 publications

(3 citation statements)

References 11 publications

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“…It is known, that if the covariant derivatives of the corresponding Riemann tensors are equal, then the covariant derivatives of the corresponding Weyl tensors are equal as well, [12]. Thus, the following theorem holds: Theorem 2.1.…”

Section: Symmetric Pairs Of Spacesmentioning

confidence: 97%

On geodesic mappings of symmetric pairs

Kiosak

Lesechko

Latysh³

2023

PIGC

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The paper treats properties of pseudo-Riemannian spaces admitting non-trivial geodesic mappings. A symmetric pair of pseudo-Riemannian spaces is a pair of spaces with coinciding values of covariant derivatives for their Riemann tensors. It is proved that the symmetric pair of pseudo-Riemannian spaces, which are not spaces of constant curvatures, are defined unequivocally by their geodesic lines. The research is carried out locally, using tensors, with no restrictions to the sign of the metric tensor and the signature of a space.

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Section: Symmetric Pairs Of Spacesmentioning

confidence: 97%

On geodesic mappings of symmetric pairs

Kiosak

Lesechko

Latysh³

2023

PIGC

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“…Asssuming that u i ı 0, choose a vector ξ i so that ξ α u α = 1. Then Thus, we have found the conditions of differential nature, which constraint the vector u i and parameters of obtained differential equation [12,16,17].…”

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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“…This criterion was used by Berezovski for the determination of the degrees of respective geodesic mappings of spaces with affine connection [12,13]; see ([9] p. 278) and also Hinterleitner for geodesic mappings of Weyl spaces [14]. One of the physical applications of the theorem is presented in [15] (it is interesting that the formulation and proof of this theorem is undertaken with the mistake mentioned above).…”

Section: Introductionmentioning

confidence: 99%

Tensor Decompositions and Their Properties

Peška,

Jukl,

Mikeš

2023

Mathematics

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In the present paper, we study two different approaches of tensor decomposition. The first part aims to study some properties of tensors that result from the fact that some components are vanishing in certain coordinates. It is proven that these conditions allow tensor decomposition, especially (1, σ), σ=1,2,3 tensors. We apply the results for special tensors such as the Riemann, Ricci, Einstein, and Weyl tensors and the deformation tensors of affine connections. Thereby, we find new criteria for the Einstein spaces, spaces of constant curvature, and projective and conformal flat spaces. Further, the proof of the theorem of Mikeš and Moldobayev is repaired. It has been used in many works and it is a generalization of the criteria formulated by Schouten and Struik. The second part deals with the properties of a special differential operator with respect to the general decomposition of tensor fields on manifolds with affine connection. It is shown that the properties of special differential operators are transferred to the components of a given decomposition.

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Models of mechanical systems preserving the Weyl tensor

Cited by 11 publications

References 11 publications

On geodesic mappings of symmetric pairs

On geodesic mappings of symmetric pairs

Special semi-reducible pseudo-Riemannian spaces

Tensor Decompositions and Their Properties

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