KaydedilenlerDerginizi ekleyin

Dergiler / Hacettepe Journal of Mathematics and Statistics / 2021 / Cilt: 50 - Sayı: 4

Statistical structures on tangent bundles and tangent Lie groups

Esmaeil Peyghan
Davood Seifipour
Aydın Gezer
Sayfa
1140–1154
Yayın Tarihi
2022-10-18
DOI
—
🏛️Bu makalenin bibliyografik verileri ve tam metin bağlantısı DergiPark üzerinden sağlanmıştır.
DergiPark Kaydı ↗
✨

Yapay Zeka Hızlı Bakış & Çıkarımlar

AI Insight
⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Series, 2018] and study statistical structures in this setting.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:Let $TM$ be a tangent bundle over a Riemannian manifold $M$ with a Riemannian metric $g$ and $TG$ be a tangent Lie group over a Lie group with a left-invariant metric $g$.
📊
Temel Bulgular & Veri:The purpose of the paper is two folds.
💡
Sonuç & Katkı:Series, 2018] and study statistical structures in this setting.
🔬Tür:Araştırma Makalesi
📍Kapsam:2018 Verileri
⚙️Değişkenler:Metric · statistical structure · tangent bundle

Abstract

Let $TM$ be a tangent bundle over a Riemannian manifold $M$ with a Riemannian metric $g$ and $TG$ be a tangent Lie group over a Lie group with a left-invariant metric $g$. The purpose of the paper is two folds. Firstly, we study statistical structures on the tangent bundle $TM$ equipped with two Riemannian $g$-natural metrics and lift connections. Secondly, we define a left-invariant complete lift connection on the tangent Lie group $TG$ equipped with metric $\tilde{g}$ introduced in [F. Asgari and H. R. Salimi Moghaddam, On the Riemannian geometry of tangent Lie groups, Rend. Circ. Mat. Palermo II. Series, 2018] and study statistical structures in this setting.

🔖

Bu Makaleye Atıf Yap

Peyghan, E., Seifipour, D., Gezer, A. (2022). Statistical structures on tangent bundles and tangent Lie groups. Hacettepe Journal of Mathematics and Statistics, Cilt: 50 - Sayı: 4, 1140–1154. https://ajindex.com/articles/529507

📄 Tam Metin PDF Okuyucu

📄

PDF görüntüleyici hazırlanıyor...

Kaynakça (17)

  1. M.T.K. Abbassi and M. Sarih, On some hereditary properties of Riemannian g-natural metrics on tangent bundles of Riemannian manifolds, Diff. Geom. Appl. 22, 19–47, 2005
  2. S. Amari, Information geometry of the EM and em algorithms for neural networks, Neural Networks, 8 (9), 1379–1408, 1995
  3. F. Asgari and H.R. Salimi Moghaddam, On the Riemannian geometry of tangent Lie groups, Rend. Circ. Mat. Palermo, II. Ser. 67 (2), 185–195, 2018
  4. V. Balan, E. Peyghan and E. Sharahi, Statistical structures on the tangent bundle of a statistical manifold with Sasaki metric, Hacet. J. Math. Stat. 49 (1), 120–135, 2020
  5. M. Belkin, P. Niyogi and V. Sindhwani, Manifold regularization: a geometric framework for learning from labeled and unlabeled examples, J. Mach. Learn. Res. 7, 2399– 2434, 2006
  6. L. Bilen and A. Gezer, Some results on Riemannian g-natural metrics generated by classical lifts on the tangent bundle, Eurasian Math. J. 8 (4), 18–34, 2017
  7. T. Fei and J. Zhang, Interaction of Codazzi couplings with (Para-)Kähler geometry, Result Math. 72 (4), 2037–2056, 2017
  8. S. Gudmundsson and E. Kappos, On the geometry of the tangent bundles, Expo. Math. 20, 1–41, 2002
  9. S. Ianus, Statistical manifolds and tangent bundles, Sci. Bull. Univ. Politechnica of Bucharest Ser. D, 56, 29–34, 1994
  10. S.L. Lauritzen, Statistical manifolds, In: Differential Geometry in Statistical Inferences, IMS Lecture Notes Monogr. Ser. 10, Inst. Math. Statist. Hayward California, 96–163, 1987
  11. H. Matsuzoe and J.I. Inoguchi, Statistical structures on tangent bundles, APPS. Appl.Sci. 5 (1), 55–57, 2003
  12. K. Nomizu and T. Sasaki, Affine Differential Geometry: Geometry of Affine Immersions, vol. 111 of Cambridge Tracts in Mathematics. Cambridge University Press, Cambridge, 1994
  13. L. Nourmohammadifar, E. Peyghan and S. Uddin, Geometry of almost Kenmotsu Hom-Lie algebras, Quaest. Math. DOI: 10.2989/16073606.2021.1886194
  14. C.R. Rao, Information and accuracy attainable in the estimation of statistical parameters, Bull. Calcutta Math. Soc. 37, 81–91, 1945
  15. A. Schwenk-Schellschmidt and U. Simon, Codazzi-equivalent affine connections, Result Math. 56, 211–229, 2009
  16. K. Sun and S. Marchand-Maillet, An information geometry of statistical manifold learning, (Proceedings of the 31st International Conference on Machine Learning (ICML-14), 1–9, 2014
  17. K. Yano, and S. Ishihara, Tangent and cotangent bundles, Marcel Dekker, Inc., New York 1973.