Ricci Solitons on 3-Symmetric Lorentzian Manifolds
Abstract
An important generalization of Einstein equations on (pseudo)Riemannian manifolds is the Ricci soliton equation which was first discussed by R. Hamilton. The solving of the Ricci soliton equation becomes possible when there are some restrictions on the structure of the manifold, or the dimension, or the class of metrics, or a class of vector fields, which appears in the Ricci soliton equation. If there is a special coordinate system, then the problem of solving the Ricci soliton equation reduces to solving a system of PDE’s. There are Brinkman coordinates on Lorentzian Walker manifolds, which are Lorentzian manifolds with a parallel (in terms of Levi-Civita) distribution of isotropic lines. This fact allows one to investigate the Ricci soliton equation on these manifolds. The geometry of Walker manifolds and Ricci solitons on them were studied by many mathematicians. In this paper, we investigate the Ricci soliton equation on 3-symmetric indecomposable Lorentzian manifolds. These manifolds have been studied by
D.V. Alekseevskii and A.S. Galaev, who have built a special local coordinate system. This article continues the authors’ study and the study of K. Honda and B. Batat, who have investigated Ricci solitons on 2-symmetric Lorentzian manifolds.
DOI 10.14258/izvasu(2018)1-21
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References
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Copyright (c) 2018 Д.Н. Оскорбин, Е.Д. Родионов, И.В. Эрнст
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