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Sibirskii Matematicheskii Zhurnal, 2019, Volume 60, Number 5, Pages 1165–1170
DOI: https://doi.org/10.33048/smzh.2019.60.513 (Mi smj3140) 		 
This article is cited in 5 scientific papers (total in 5 papers)

Ricci solitons and Killing fields on generalized Cahen–Wallach manifolds

D. N. Oskorbin, E. D. Rodionov

Altai State University, Barnaul, Russia
Full-text PDF (382 kB) Citations (5)
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DOI: https://doi.org/10.33048/smzh.2019.60.513
Abstract: We study Ricci solitons and Killing fields on generalized Cahen–Wallach manifolds. The Ricci soliton equation provides a generalization of the Einstein equation on (pseudo-)Riemannian manifolds which is closely connected with Ricci flows. We prove that the Ricci soliton equation is locally solvable with any constant in the Ricci soliton equation on generalized Cahen–Wallach manifolds. Using a Brinkmann coordinate system, we study the Killing fields on these manifolds and give constraints on the dimension of the space of Killing fields. Also, we obtain solutions to the Killing equations for 2-symmetric Lorentzian manifolds in small dimensions.
Keywords: Ricci soliton, Killing field, generalized Cahen–Wallach manifold, Brinkmann coordinate system.
Received: 15.04.2019
Revised: 28.06.2019
Accepted: 24.07.2019
English version:
Siberian Mathematical Journal, 2019, Volume 60, Issue 5, Pages 911–915
DOI: https://doi.org/10.1134/S0037446619050136
Bibliographic databases:
Document Type: Article
UDC: 514.765
Language: Russian
Citation: D. N. Oskorbin, E. D. Rodionov, “Ricci solitons and Killing fields on generalized Cahen–Wallach manifolds”, Sibirsk. Mat. Zh., 60:5 (2019), 1165–1170; Siberian Math. J., 60:5 (2019), 911–915
Citation in format AMSBIB
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    • This publication is cited in the following 5 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Сибирский математический журнал Siberian Mathematical Journal
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