On the properties of Ricci solitons

Kiosak, V.; Savchenko, A. M.; Kusik, L. I.

doi:10.1063/5.0100792

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Lemma 32 In Recurrent Kähler Spaces the Following Conditions...1

Discussion1

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2023

2024

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Cited by 2 publications

(2 citation statements)

References 17 publications

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“…Note that the equations (3.14) coincide with the integrability conditions for the equation defining φ(Ric)-vector fields and Ricci solitons [1,2,5,12,14,18].…”

Section: Lemma 32 In Recurrent Kähler Spaces the Following Conditions...mentioning

confidence: 88%

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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“…Note that the equations (3.14) coincide with the integrability conditions for the equation defining φ(Ric)-vector fields and Ricci solitons [1,2,5,12,14,18].…”

Section: Lemma 32 In Recurrent Kähler Spaces the Following Conditions...mentioning

confidence: 88%

Conformal recurrent Kӓhler spaces

Savchenko,

Shevchenko,

Hedulian

2024

PIGC

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“…There are many other spaces admitting geodesic mappings only under additional assumptions them which can have inner or other nature. Moreover, for example, Einstein spaces for n ą 4, quasi-Einstein spaces, and Ricci solitons admit non-trivial geodesic mappings only under certain restrictions on vectors of main equations [1,4,5,9,11,17,22]. Also four-dimensional Einstein spaces, symmetric spaces, geodesic symmetric spaces [3] admit non-trivial geodesic mappings if they are spaces of constant curvature.…”

Section: Discussionmentioning

confidence: 99%

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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On the properties of Ricci solitons

Cited by 2 publications

References 17 publications

Conformal recurrent Kӓhler spaces

Conformal recurrent Kӓhler spaces

On geodesic mappings of symmetric pairs

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