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.

中文翻译：

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2-对称不可分解洛伦兹流形上的共形消杀向量场

摘要

Killing向量场的一个自然推广是共形Killing向量场，它在流形的共形变换群、流形上的Ricci流以及Ricci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Killing向量场。可以确定的是，Killing 方程的共形类似物的共形因子取决于 Weyl 张量的行为。此外，在 Weyl 张量等于 0 的情况下，使用 Airy 函数构造具有可变共形因子的共形 Kill 向量场的重要示例。