On Conformally Killing Vector Fields on a 2-Symmetric Indecomposable Lorentzian Manifold

IF 0.5 Q3 MATHEMATICS

Russian Mathematics Pub Date : 2024-01-09 DOI:10.3103/s1066369x23100055

M. E. Gnedko, D. N. Oskorbin, E. D. Rodionov

引用次数: 0

Abstract

A natural generalization of Killing vector fields is conformally Killing vector fields, which play an important role in the study of the group of conformal transformations of manifolds, Ricci flows on manifolds, and the theory of Ricci solitons. In this paper, conformally Killing vector fields are studied on 2-symmetric indecomposable Lorentzian manifolds. It is established that the conformal factor of the conformal analogue of the Killing equation on them depends on the behavior of the Weyl tensor. In addition, in the case when the Weyl tensor is equal to zero, nontrivial examples of conformally Killing vector fields with a variable conformal factor are constructed using the Airy functions.

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论 2 对称不可分解洛伦兹积分形上的共形起宁向量场

摘要基林向量场的一个自然概括是共形基林向量场，它在流形的共形变换群、流形上的利玛窦流以及利玛窦孤子理论的研究中发挥着重要作用。本文研究了 2 对称不可分解洛伦兹流形上的共形基林向量场。研究证明，基林方程的共形模拟的共形因子取决于韦尔张量的行为。此外，在韦尔张量等于零的情况下，利用艾里函数构造了具有可变共形因子的共形基林向量场的非微观例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Russian Mathematics MATHEMATICS-

CiteScore

0.90

自引率

25.00%

发文量

期刊介绍： Russian Mathematics is a peer reviewed periodical that encompasses the most significant research in both pure and applied mathematics.