具有1/4对称度量联络的Kenmotsu流形上的(0,2)型对称平行张量场

吉林大学学报(理学版) ›› 2022, Vol. 60 ›› Issue (2): 311-315.

具有1/4对称度量联络的Kenmotsu流形上的(0,2)型对称平行张量场

潘鹏

西北师范大学数学与统计学院, 兰州 730070

收稿日期:2021-07-22 出版日期:2022-03-26 发布日期:2022-03-26
通讯作者: 潘鹏 E-mail:369777436@qq.com

Symmetric Parallel (0,2)-Type Tensor Fields on Kenmotsu Manifolds with a Quarter-Symmetric Metric Connection

PAN Peng

College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Received:2021-07-22 Online:2022-03-26 Published:2022-03-26

摘要/Abstract

摘要： 利用张量分析方法, 结合Kenmotsu流形的结构方程, 考虑关于1/4对称度量联络平行的对称(0,2)型张量场的Eisenhart问题, 在适当条件下证明该张量场必为度量张量的常数倍, 并给出一个Ricci对称的Kenmotsu流形为Einstein流形的充要条件.

关键词: 1/4对称度量联络, Kenmotsu流形, Eisenhart问题

Abstract: The author considered the Eisenhart problem of symmetric parallel (0,2)-type tensor fields with respect to a quarter-symmetric metric connection by using tensor analysis method and Kenmotsu manifold’s structural equations. Under suitable conditions, the author proved that the tensor field must be a constant multiple of the metric tensor, and gave a necessary and sufficient condition for a Ricci symmetric Kenmotsu manifold to be an Einstein manifold.

Key words: quarter-symmetric metric connection, Kenmotsu manifold, Eisenhart problem

中图分类号:

O186.12

潘鹏. 具有1/4对称度量联络的Kenmotsu流形上的(0,2)型对称平行张量场[J]. 吉林大学学报(理学版), 2022, 60(2): 311-315.

PAN Peng. Symmetric Parallel (0,2)-Type Tensor Fields on Kenmotsu Manifolds with a Quarter-Symmetric Metric Connection[J]. Journal of Jilin University Science Edition, 2022, 60(2): 311-315.