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《山东大学学报(理学版)》 ›› 2021, Vol. 56 ›› Issue (11): 105-110.doi: 10.6040/j.issn.1671-9352.0.2021.156

• • 上一篇    

关于双曲空间上Kenmotsu统计结构的一个结果

蒋岩,吴凤,张量*   

  1. 安徽师范大学数学与统计学院, 安徽 芜湖 241000
  • 发布日期:2021-11-15
  • 作者简介:蒋岩(1996— ),女,硕士研究生,研究方向为微分几何. E-mail:2308409981@qq.com*通信作者简介:张量(1979— ),男,硕士,副教授,硕士生导师,研究方向为微分几何. E-mail:zhliang43@163.com
  • 基金资助:
    安徽师范大学博士启动基金项目(751841)

A result on Kenmotsu statistical structures on a hyperbolic space

JIANG Yan, WU Feng, ZHANG Liang*   

  1. School of Mathematics and Statistics, Anhui Normal University, Wuhu 241000, Anhui, China
  • Published:2021-11-15

摘要: 双曲空间是截曲率为负常数的Riemann流形。特别地,截面曲率为-1的奇数维双曲空间H 2n+1上有经典的Kenmotsu结构。证明了H 2n+1在经典Kenmotsu结构基础之上不存在非平凡的φ-曲率为常数的Kenmotsu统计结构。

关键词: 双曲空间, Kenmotsu统计流形, 常φ, -曲率

Abstract: Hyperbolic space is a Riemannian manifold with constant negative sectional curvature. In particular, an odd-dimensional hyperbolic space H 2n+1 with sectional curvature -1 can be endowed with the classical Kenmotsu structure. In this paper, we prove that on H 2n+1 there exists no non-trivial Kenmotsu statistical structure with constant φ-curvature based on the classical Kenmotsu structure.

Key words: hyperbolic space, Kenmotsu statistical manifold, constant φ, -curvature

中图分类号: 

  • O186.12
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[1] 吴凤,张量. 关于常φ -曲率Sasaki统计流形的一些结果[J]. 《山东大学学报(理学版)》, 2021, 56(4): 86-93.
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