Ricci Solitons on 3-Symmetric Lorentzian Manifolds

  • Д.Н. Оскорбин Алтайский государственный университет (Барнаул, Россия)
  • Е.Д. Родионов Алтайский государственный университет (Барнаул, Россия)
  • И.В. Эрнст Алтайский государственный университет (Барнаул, Россия)
Keywords: Ricci soliton, Walker manifold, Lorentzian manifold, fc-symmetric manifold, coordinate system

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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Author Biographies

Д.Н. Оскорбин, Алтайский государственный университет (Барнаул, Россия)
кандидат физико-математических наук, доцент кафедрыматематического анализа Алтайского государственного университета
Е.Д. Родионов, Алтайский государственный университет (Барнаул, Россия)
доктор физико-математических наук, профессор кафедры математического анализа Алтайского государственного университета
И.В. Эрнст, Алтайский государственный университет (Барнаул, Россия)
студент факультета математики и информационных технологий Алтайского государственного университета

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Published
2018-03-06
How to Cite
Оскорбин, Д., Родионов, Е., & Эрнст, И. (2018). Ricci Solitons on 3-Symmetric Lorentzian Manifolds. Izvestiya of Altai State University, (1(99), 119-122. https://doi.org/https://doi.org/10.14258/izvasu(2018)1-21
Section
Математика и механика

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