Geodesic mappings of compact quasi-Einstein spaces, II

Kiosak, V.; Savchenko, A. M.; Latysh, O.

doi:10.15673/tmgc.v14i1.1936

Cited by 14 publications

(8 citation statements)

References 17 publications

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“…If a equidistant pseudo-Riemannian space V n admits generalized φ(Ric)-vector fields, then in this space the conditions (3.10) hold for a vector φ i and conditions (3.12) for the Einstein tensor. Theorem 3.1 agrees well with the results of [12,17,18], when the latter are widened by application of the concept of the generalized φ(Ric)-vector fields.…”

Section: Generalized φ(Ric)-vector Spaces In Equidistant Spacessupporting

confidence: 83%

Generalized φ(Ric)-vector fields in special pseudo-Riemannian spaces

Vashpanova¹,

Savchenko²,

Vasylieva³

2021

PIGC

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The paper treats pseudo-Riemannian spaces permitting generalized φ(Ric)-vector fields. We study conditions for the existence of such vector fields in conformally flat, equidistant, reducible and Kählerian pseudo-Riemannian spaces. The obtained results can be applied for the construction of generalized φ(Ric)-vector fields that differ from φ(Ric)-vector fields. The research is carried out locally without limitations imposed on a sign of metric tensor.

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Section: Generalized φ(Ric)-vector Spaces In Equidistant Spacessupporting

confidence: 83%

Generalized φ(Ric)-vector fields in special pseudo-Riemannian spaces

Vashpanova¹,

Savchenko²,

Vasylieva³

2021

PIGC

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“…Equidistant spaces are closed in relation to non-trivial geodesic mappings. The application of a supplementary tensor allows to study simultaneously the properties of a pair of pseudo-Riemannian spaces in geodesic correspondence, [7,16,18].…”

Section: Discussionmentioning

confidence: 99%

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

Кіосак¹,

Пришляк

Lesechko

2021

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В роботі досліджуються два псевдоріманових простори, які мають спільні геодезичні лінії. Вимагається виконання умов алгебраїчного та диференціального характеру на тензор Рімана одного з них. А операція опускання індексів та обчислення коваріантної похідної здійснюється відносно метрики та об'єктів зв'язності іншого простору. Для досліджень використовується спеціальний допоміжний тензор. Доведено, що виконання додаткових умов приводить до просторів, що не допускають нетривіальних геодезичних відображень, або простори належать до еквідістантних просторів. Використовуються тензорні методи без обмежень на знак метрики.

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“…Pseudo-Riemannian spaces satisfying (4.12) are called quasi-Einstein. Their geodesic mappings and other geometric properties were studied in [2,[6][7][8]10].…”

Section: Geodesic Symmetric Pairsmentioning

confidence: 99%

On geodesic mappings of symmetric pairs

Kiosak

Lesechko

Latysh³

2023

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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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Geodesic mappings of compact quasi-Einstein spaces, II

Cited by 14 publications

References 17 publications

Generalized φ(Ric)-vector fields in special pseudo-Riemannian spaces

Generalized φ(Ric)-vector fields in special pseudo-Riemannian spaces

On the geodesic mappings of pseudo-Riemannian spaces with special supplementary tensor

On geodesic mappings of symmetric pairs

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