Left Invariant Harmonic Vector Fields on Solvable Lie Groups  

可解李群上的左不变调和向量场

作　　者：Zhang Mengxue Tan Ju Sun Bichao 张孟雪;谭举;孙必超(安徽工业大学微电子与数据科学学院,安徽马鞍山243032;工业大数据分析与智能决策安徽省联合共建学科重点实验室,安徽马鞍山243032)

机构地区：[1]School of Microelectronics and Data Science,Anhui University of Technology,Maanshan 243032,China [2]Anhui Provincial Joint Key Laboratory of Disciplines for Industrial Big Data Analysis and Intelligent Decision,Maanshan 243032,China

出　　处：《南开大学学报（自然科学版）》2024年第5期115-120,共6页Journal of Nankai University(Natural Sience)

基　　金：Supported by General Project for the Cultivation of Excellent Young Teachers of Anhui Province(YQYB2024018)。

摘　　要：It's shown that on an n-dimensional LCS Lie group,there exist harmonic sections and left invariant vector fields defining harmonic maps only when it is endowed with a flat left invariant pseudo-Riemannian metric.Moreover,we determine all the vector fields which are critical points of the energy functional restricted to vector fields of the same length on the n-dimensional pseudo-Riemannian LCS Lie group.证明了在n维LCS李群上,只有当它被赋予平坦的左不变伪黎曼度量时,才存在调和截面以及定义调和映射的左不变向量场.此外,在n维伪黎曼LCS李群上得到了这样的向量场,它们是被限制在相同长度的向量场上的能量泛函的临界点.

关 键 词：harmonic vector fields harmonic maps Lie group 

分 类 号：O152.5[理学—数学]