Journal of Lanzhou University of Technology ›› 2025, Vol. 51 ›› Issue (3): 161-166.

• Scientific • Previous Articles     Next Articles

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

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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