具有半对称度量ρ-联络的共形平坦Yamabe孤立子的特征  

Characteristics of Conformally Flat Yamabe Soliton withSemi-symmetric Metricρ-Connection

作　　者：潘鹏 刘建成 PAN Peng;LIU Jiancheng(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2021年第5期1045-1049,共5页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金(批准号:11761061);甘肃省高等学校创新能力提升项目(批准号:2019B-045);甘肃省科技计划项目(批准号:20JR5RA515)

摘　　要：利用Riemann流形上的微分算子、协变导数算子和Lie导数算子的性质及曲率张量场公式,讨论在紧致条件下具有半对称度量ρ-联络的n(n>3)维共形平坦Yamabe孤立子的特征,并给出具有该结构的Yamabe孤立子截面曲率为常数的一个充要条件.结果表明,具有该结构的Yamabe孤立子的截面曲率为常数-1,孤立子常数为-n(n-1),且孤立子场为Killing型向量场.By using the properties of differential operators,covariant derivative operator,Lie-derivative operator and the expressions of curvature tensor fields on Riemannian manifold,we discussed the characteristics of n(n>3)-dimensional conformally flat Yamabe soliton with the semi-symmetric metricρ-connection under compact condition,and gave a necessary and sufficient condition that sectional curvature of Yamabe sotion with this structure was constant.The results show that the sectional curvature of Yamabe soliton with this structure is constant-1,the soliton constant is-n(n-1),and the soliton field is a Killing vector field.

关 键 词：半对称度量ρ-联络 共形向量场 Yamabe孤立子 Weyl张量 Killing型向量场 

分 类 号：O186.12[理学—数学]