一类三维非单模洛伦兹李群上的代数Ricci孤立子

A Class of Algebraic Ricci Solitons on a Three-Dimensional Non-Unimodular Left-Invariant Lorentzian Lie Group

摘要: Ricci孤立子是一类特殊的黎曼度量，类似于Ricci曲率定号流形，是近些年研究的热点。关于具有积结构的三维洛伦兹李群与两种联络有关的代数Ricci孤立子存在情况，有学者已经给出了明确的结论。本文在现有成果的基础上，将其拓展到具体一类三维非单模左不变洛伦兹李群上与三种联络相关的两类代数Ricci孤立子存在的情形，给出了该群分别与三种联络有关的两类代数Ricci孤立子存在条件的具体结果，这对揭示李群上几何性质和拓扑性质有重要的理论研究意义。

Abstract: Ricci solitons are a special class of Riemannian metrics that resemble curvature-numbered manifolds, which has been a hot topic in recent years. Some scholars have come to a definite conclusion about the existence of algebraic solitons related to the three-dimensional Lorentzian Lie group with product structure and two kinds of connections. On the basis of the existing results, this paper expands it to a specific type of three-dimensional non-unimodular left-invariant Lorentzian Lie group and two types of algebraic soliton related to three kinds of connections. We gives the specific conditions for the existence of two types of algebraic solitons related to the three types of connections, which has important theoretical research significance for revealing the geometric and topological properties of the Lie group.