publication . Article . 2017

Ricci Solitons on 2-Symmetric Four-Dimensional Lorentzian Manifolds

Оскорбин, Д. Н.; Родионов, Е. Д.; Эрнст, И.В.;
Open Access Russian
  • Published: 01 Nov 2017 Journal: Izvestiya of Altai State University (issn: 1561-9451, eissn: 1561-9443, Copyright policy)
  • Publisher: Izvestiya of Altai State University
An important generalization of Einstein metrics on a (pseudo) Riemannian manifolds are Ricci solitons first discussed by R. Hamilton. The problem of finding Ricci solitons is quite difficult, so we assume the restriction of one of the following: the structure of the manifold, the dimension, the class of metrics, or a class of vector fields, participating in the Ricci soliton equation. The most important examples of such restrictions are 2-symmetric Lorentzian manifolds investigated by A.S. Galaaev, D.V. Alekseevskii, and J.M. Senovilla. 2-Symmetric locally indecomposable Lorentzian manifolds have parallel null-distribution, i.e. they are Walker manifolds. These ...
arXiv: Mathematics::Differential GeometryNonlinear Sciences::Pattern Formation and Solitons

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