Geodesic mappings of compact quasi-Einstein spaces with constant scalar curvature

Kiosak, V.; Savchenko, A. M.; Kamienieva, A.

doi:10.1063/5.0033661

Cited by 16 publications

(8 citation statements)

References 19 publications

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“…The works [4,5,7] are devoted to the research on geodesic mappings of quasi-Einstein spaces with gradient defining vector. The above-mentioned spaces are divided into three types: main, particular and special [1].…”

Section: Introductionmentioning

confidence: 99%

Geodesic mappings of compact quasi-Einstein spaces, II

Kiosak¹,

Savchenko²,

Latysh³

2021

PIGC

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The paper treats geodesic mappings of quasi-Einstein spaces with gradient defining vector. Previously the authors defined three types of these spaces. In the present paper it is proved that there are no quasi-Einstein spaces of special type. It is demonstrated that quasi-Einstein spaces of main type are closed with respect to geodesic mappings. The spaces of particular type are proved to be geodesic $D$-symmetric spaces.

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Section: Introductionmentioning

confidence: 99%

Geodesic mappings of compact quasi-Einstein spaces, II

Kiosak¹,

Savchenko²,

Latysh³

2021

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“…Those conditions are usually used for specialization of spaces. However lowering down of the indices is defined by a metric tensor of V n , while covariant derivative is calculated by a connection of V n , [13][14][15].…”

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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“…It turns out that in all the cases those pseudo-Riemannian spaces are quasi-Einstein pseudo-Riemannian spaces. Geodesic and conformal mappings of these spaces are studied in [12,15,16]. The obtained results can be applied for the construction and further research on geometric properties of these spaces.…”

Section: Discussionmentioning

confidence: 99%

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

Vashpanova¹,

Savchenko²,

Vasylieva³

2021

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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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Geodesic mappings of compact quasi-Einstein spaces with constant scalar curvature

Cited by 16 publications

References 19 publications

Geodesic mappings of compact quasi-Einstein spaces, II

Geodesic mappings of compact quasi-Einstein spaces, II

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

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

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