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Some non-trivial and non-gradient closed pseudo-Riemannian steady Ricci solitons
Maryam Jamreh, Mehdi Nadjafikhah School of Mathematics, Iran University of Science and Technology, Narmak, Tehran 16846-13114, Iran
Аннотация:
In this paper, we study the Ricci soliton equation on compact indecomposable Lorentzian $3$-manifolds that admit a parallel light-like vector field with closed orbits. These compact structures that are geodesically complete, admit non-trivial, i.e., non-Einstein and non-gradient steady Lorentzian Ricci solitons with zero scalar curvature which show the difference between closed Riemannian and pseudo-Riemannian Ricci solitons. The associated potential vector field of a Ricci soliton structure in all the cases that we construct on these manifolds is a space-like vector field. However, we show that there are examples of closed pseudo-Riemannian steady Ricci solitons in the neutral signature $(2,2)$ with zero scalar curvature such that the associated potential vector field can be time-like or null. These compact manifolds are also geodesically complete and they cannot admit a conformal-Killing vector field.
Ключевые слова и фразы:
Ricci solitons, closed pseudo-Riemannian manifolds, parallel light-like vector field.
Поступила в редакцию: 10.10.2018 Исправленный вариант: 13.05.2019
Образец цитирования:
Maryam Jamreh, Mehdi Nadjafikhah, “Some non-trivial and non-gradient closed pseudo-Riemannian steady Ricci solitons”, Журн. матем. физ., анал., геом., 15:4 (2019), 526–542
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/jmag742 https://www.mathnet.ru/rus/jmag/v15/i4/p526
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Страница аннотации: | 53 | PDF полного текста: | 39 | Список литературы: | 9 |
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