논문KCI 등재
A note on statistical manifolds with torsion
0
조회
0
다운로드
2
인용
0
참고문헌
키워드
주제분류수학
초록
Given a linear connection $\nabla$ and its dual connection $\nabla^*$, we discuss the situation where $\nabla +\nabla^* = 0$. We also discuss statistical manifolds with torsion and give new examples of some type for linear connections inducing the statistical manifolds with non-zero torsion.
Abstract
Given a linear connection $\nabla$ and its dual connection $\nabla^*$, we discuss the situation where $\nabla +\nabla^* = 0$. We also discuss statistical manifolds with torsion and give new examples of some type for linear connections inducing the statistical manifolds with non-zero torsion.
참고문헌 (13)
- I. Agricola, "The Srn´ı lectures on non-integrable geometries with torsion", Arch. Math. (Brno), 42(suppl), pp.5~84 (2006)
- S. Amari, "Information geometry and its applications, Applied Mathematical Sciences, 194" (2016), Springer
- A. M. Blaga, "Conformal-projective transformations on statistical and semi-Weyl manifolds with torsion", arXiv.2209.00689vl, ~ (2022)
- O. Calin, "Geometric Modeling in Probability and Statistics" (2013), Springer
- E. Cartan, "Sur les vari´et´es `a connexion affine, et la th´eorie de la relativit´e g´en´eralis´ee (deuxi`eme partie)", Ann. Sci. ´Ecole Norm. Sup. (3), 42, pp.17~88 (1925)
- A. Friedmann, "¨ Uber die Geometrie der halbsymmetrischen ¨ Ubertragungen", Math. Z, 21(1), pp.211~223 (1924)[DOI]
- T. Kurose, "Geometry and Something" (2007)
- S. L. Lauritzen, "Statistical manifolds", Differential Geometry in Statistical Inference, 10, pp.163~216 (1987)
- H. Matsuzoe, "Statistical manifolds and affine differential geometry, in Probabilistic approach to geometry, Adv. Stud. Pure Math., 57", pp.303~321 (2010), Math. Soc. Japan
- Differential geometry of smooth families of probability distributions, "H. Nagaoka", Dept. of Math. Eng. and Instr. Phys., Univ. of Tokyo, ~, pp.Technical Report (METR) 82–7 (1982)
- A. P. Norden, "On pairs of conjugate parallel displacements in multidimensional spaces", Doklady Akademii nauk SSSR, 49, pp.1345~1347 (1945)
- U. Simon, "Handbook of differential geometry, Vol. I", pp.905~961 (2000), North-Holland
- F. Tricerri, "Homogeneous structures on Riemannian manifolds, London Mathematical Society Lecture Note Series, 83" (1983), Cambridge University Press
관련 논문AI추천
A remark on statistical manifolds with torsion김화정강원경기수학회 · 한국수학논문집2023 · 제31권 제2호Curvatures of semi-symmetric metric connections on statistical manifoldsMohammad Bagher Kazemi Balgeshir, Shiva Salahvarzi대한수학회 · 대한수학회논문집2021 · 제36권 제1호Some properties of critical point equations metrics on the statistical manifoldsHajar Ghahremani-Gol, Mohammad Amin Sedghi대한수학회 · 대한수학회논문집2024 · 제39권 제2호On Some Properties of Riemannian Manifolds with a Generalized ConnectionAzam Etemad Dehkordy경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제4호On a Type of Semi-Symmetric Non-Metric Connection on Riemannian ManifoldsAjit Barman경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2015 · 제55권 제3호Results concerning semi-symmetric metric $F$-connections on the Hsu-$B$ manifoldsAydin Gezer, Cagri Karaman, Uday Chand De대한수학회 · 대한수학회논문집2023 · 제38권 제3호
이 간행물의 다른 논문 (23건)
Estimates for certain shifted convolution sums involving Hecke eigenvaluesGuodong Huapp. 319-330MAXIMAL CHAIN OF IDEALS AND n-MAXIMAL IDEALHemin A. Ahmad, Parween A. Hummadipp. 331-340Simple formulations on circulant matrices with alternating FibonacciSugi Guritmanpp. 341-354Unitary analogues of a generalized number-theoretic sumTraiwat Intarawong, Boonrod Yuttananpp. 355-364On graded $J$-ideals over graded ringsTamem Al-Shorman, Ece Yetkin Celikel, Malik Batainehpp. 365-376