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.
出处
《南开大学学报（自然科学版）》
CAS
CSCD
北大核心
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)。
作者简介
Zhang Mengxue(1998-),female,native place:Anhui Maanshan;Corresponding author:Tan Ju(1987-),male,native place:Anhui Maanshan,associate professor,direction of research:Lie group,Lie algebra and differential geometry.E-mail:tanju2007@163.com。
