兰州理工大学学报 ›› 2025, Vol. 51 ›› Issue (3): 161-166.

• 数理科学 • 上一篇    下一篇

共形射影等价的统计流形及其仿射浸入

徐晓利1, 王瑜*2, 秦华军3   

  1. 1.中国人民武装警察部队警官学院 基础部, 四川 成都 610213;
    2.海南师范大学 数学与统计学院, 海南 海口 571127;
    3.四川师范大学 数学科学学院, 四川 成都 610066
  • 收稿日期:2023-12-26 出版日期:2025-06-28 发布日期:2025-06-30
  • 通讯作者: 王 瑜(1980-),女,河南漯河人,教授.Email:wangyu_813@163.com
  • 基金资助:
    国家自然科学基金(12071322),四川省科技计划项目(2022JDTD0019),四川省重点实验室项目(2022QYJ04,2023QYJ05)

Conformal-projectively equivalence of statistical manifolds and its affine immersion

XU Xiao-li1, WANG Yu2, QIN Hua-jun3   

  1. 1. Department of Basic Courses, Officers’ College of People’s Armed Police, Chengdu 610213, China;
    2. School of Mathematics and Statistics, Hainan Normal University, Haikou 571127, China;
    3. School of Mathematical Sciences, Sichuan Normal University,Chengdu 610066, China
  • Received:2023-12-26 Online:2025-06-28 Published:2025-06-30

摘要: 具有平坦结构或者具有共形射影平坦结构的统计流形是信息几何研究的主要对象, 研究统计流形的共形射影等价性,并得到几条性质,同时研究了余维为2的相对仿射浸入,得到不同的浸入方式导出的统计结构的关系.

关键词: 统计流形, 对偶联络, 等仿射结构, 共形射影等价, 仿射浸入

Abstract: Statistical manifolds with a flat structure or a conformal projective flat structure are the main objects studied in information geometry. The conformal projective equivalence of statistical manifolds is investigated, and several properties are obtained. Meanwhile, relative affine immersions with codimension 2 are studied, and the relationships between statistical structures derived from different immersion methods are obtained.

Key words: statistical manifolds, dual connection, equiaffine structure, conformal projective, affine immersion

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