SavedAdd your journal

Journals / International Electronic Journal of Geometry / 2026 / Volume: 19 Issue: 1

$\alpha$-Jacobi Type Vector Fields in Hyperbolic 3-space with Natural Statistical Structure

Oleksandr Sadokha(ULUDAĞ ÜNİVERSİTESİ)
Cengizhan Murathan(ULUDAĞ ÜNİVERSİTESİ)0000-0002-2273-3243
Pages
—
Publication Date
2026-04-22
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

The study is a natural extension of the results obtained by Wang and Zhang, [16], under the classical Levi-Civita connection.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper, we fully determine all Jacobi-type vector fields in hyperbolic three-space by taking advantage of both its constant negative curvature and its intrinsic compatibility with statistical manifold structures.
📊
Key Findings & Data:In this paper, we fully determine all Jacobi-type vector fields in hyperbolic three-space by taking advantage of both its constant negative curvature and its intrinsic compatibility with statistical manifold structures.
💡
Conclusion & Impact:The study is a natural extension of the results obtained by Wang and Zhang, [16], under the classical Levi-Civita connection.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Statistical manifolds · statistical models · Jacobi type vector fields

Abstract

In this paper, we fully determine all Jacobi-type vector fields in hyperbolic three-space by taking advantage of both its constant negative curvature and its intrinsic compatibility with statistical manifold structures. The study is a natural extension of the results obtained by Wang and Zhang, [16], under the classical Levi-Civita connection.

🔖

Cite This Article

Sadokha, O., Murathan, C. (2026). $\alpha$-Jacobi Type Vector Fields in Hyperbolic 3-space with Natural Statistical Structure. International Electronic Journal of Geometry, Volume: 19 Issue: 1. https://doi.org/10.36890/iejg.1847502

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (18)

  1. Addad, K. and Ouakkas, S.: On the α-connections and the α-conformal equivalence on statistical manifolds. Arab Journal of Mathematical Sciences. 30(1), 2-15 (2024).
  2. Amari, S.: Differential-Geometrical Methods in Statistics, Lecture Notes in Statistics,vol. 28. Springer, Berlin (1985).
  3. Arif, M.S., Er-chuan, Z., Hua-fei, S.: Jacobi fields on the manifold of Freund. Ital. J. Pure Appl. Math. 34, 181-188 (2015).
  4. Cafaro, C., Ali, S. A.: Jacobi fields on statistical manifolds of negative curvature(English summary). Phys. D. 234(1), 70-80 (2007).
  5. Costa, S. I., Santos, S. A., Strapasson, J. E.: Fisher information distance. Ageometrical reading. Discrete Applied Mathematics. 197, 59-69 (2015). https://doi.org/10.1016/j.dam.2014.10.004. 6
  6. Deshmukh, S.: Jacobi-type vector fields on Ricci soliton. Bull. Math. Soc. Sci. Math. Roum. 55(1), 41-50 (2012).
  7. Fujitani, Y.: Information geometry of warped product spaces. Info. Geo. 6, 127-155 (2023). https://doi.org/10.1007/s41884-022-00091-9
  8. Lauritzen, S.: In statistical manifolds. In: Differential Geometry in Statistical Inference Amari, S.,Barndorff-Nielsen, O., Kass, R., Lauritzen, S., Rao, C.R. eds.IMS Lecture NotesInstitute of Mathematical Statistics, Hayward (1987).
  9. Lê, H. V.: Statistical manifolds are statistical models. Journal of Geometry, 84, 83-93 (2006).
  10. Nomizu, K., Simon, U.: Notes on conjugate connections. In: Geometry and topology of submanifolds, IV Proceedings of the Conference on Differential Geometry and Vision June 27-29 1991, Leuven, BELGIUM. 152-173 (1992).
  11. Opozda, B.: A sectional curvature for statistical structures. Linear Alg. Appl. 497, 134-161 (2016).
  12. Rao, C.R.:Information and accuracy attainable in the estimation of statistical parameters. Bull. Calcutta Math. Soc. 37, 81-91 (1945).
  13. Shima, H.: The geometry of Hessian Structures. World Scientific Publishing Co. Pte. Ltd. (2007).
  14. Simon, U.: Affine Differential Geometry. In: Handbook of Differential Geometry, Dillen, F., Verstraelen, L., Eds. North-Holland, Amsterdam (2000).
  15. Takano, K.: Geodesics on statistical models of the multivariate normal distribution. Tensor, N. S. 67, 162-169 (2006).
  16. Wang, Y., Zhang, Y.: Jacobi-type Vector Fields on H3 and R3. Aims Mathematics. 6 (11), 11894-11903 (2021). https://doi.org/10.3934/math.2021690
  17. Zhang, J.:Divergence function, duality, and convex analysis. Neural Comput. 16, 159-195 (2004).
  18. Costa, S. I., Santos, S. A., Strapasson, J. E.: Fisher information distance. Ageometrical reading. Discrete Applied Mathematics. 197, 59-69 (2015). https://doi.org/10.1016/j.dam.2014.10.004. 6