پیوندهای مفید
آمار
| تعداد نشریات | 22 |
| تعداد شمارهها | 717 |
| تعداد مقالات | 10,297 |
| تعداد مشاهده مقاله | 72,204,864 |
| تعداد دریافت فایل اصل مقاله | 63,942,429 |
How many statistical structures and Ricci flat affine connections are there on the tangent bundle? | ||
| International Journal of Nonlinear Analysis and Applications | ||
| مقاله 19، دوره 15، شماره 1، فروردین 2024، صفحه 225-239 اصل مقاله (452.46 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22075/ijnaa.2023.29053.4052 | ||
| نویسندگان | ||
| Esmaeil Peyghan* 1؛ Farshad Firuzi2؛ Uday Chand De3 | ||
| 1Department of Mathematics, Faculty of Science, Arak University, Arak, 38156-8-8349, Iran | ||
| 2Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran | ||
| 3Department of Pure Mathematics, Calcutta University, 35, B.C.Road, Kolkata-700019, India | ||
| تاریخ دریافت: 28 آبان 1401، تاریخ بازنگری: 24 بهمن 1401، تاریخ پذیرش: 10 فروردین 1402 | ||
| چکیده | ||
| In this paper, we consider the tangent bundle TM of a Riemannian manifold (M, g) with the Sasaki metric G and using the Cauchy-Kowalevski Theorem, we answer the question of how many analytic statistical structures are there on (TM, G). Also, we study the Ricci tensor of linear affine connections on the tangent bundle TM. In addition, we answer the question of how many Ricci flat affine connections with and without torsion are there on the tangent bundle. | ||
| کلیدواژهها | ||
| Cauchy-Kowalevski Theorem؛ Sasaki Metrics؛ Statistical Structures | ||
| مراجع | ||
|
[1] K.M.T. Abbassi and M. Sarih, On natural metrics on tangent bundles of Riemannian manifolds, Arch. Math. (Brno) 41 (2005), 71–92. [2] S. Akbulut, M. Ozdemir and A.A. Salimov, Diagonal lift in the cotangent bundle and its applications, Turk. J. Math. 25 (2001), 491–502. [3] S. Amari, Information geometry on hierarchy of probability distributions, IEEE Trans. Inform. Theory, 47 (2001), no. 5, 1701–1711. [4] S. Amari, Information geometry of the EM and em algorithms for neural networks, Neural Networks 8 (1995), no. 9, 1379–1408. [5] V. Balan, E. Peyghan and E. Sharahi, Statistical structures on tangent bundle of a statistical manifold with Sasaki metric, Preprint. [6] M. Belkin, P. Niyogi and V. Sindhwani, Manifold regularization: a geometric framework for learning from labeled and unlabeled examples, J. Machine Learn. Res. 7 (2006), 2399–2434. [7] D.E. Blair, Riemannian Geometry of Contact and Symplectic Manifolds, Second Edition. Progress in Mathematics 203, Birkh¨auser, Boston, 2010. [8] Z. Duˇsek and O. Kowalski, How many Ricci flat affine connections are there with arbitrary torsion?, Publ. Math. Debrecen, 88 (2016), no. 4, 511–516. [9] R. B. Gardner and G. R. Wilkens, The fundamental theorems of curves and hypersurfaces in centro-affine geometry, Bull. Belg. Math. Soc. Simon Stevin 4 (1997), 379–401. [10] A. Gezer and M. Ozkan, Notes on the tangent bundle with deformed complete lift metric, Turk. J. Math., 38 (2014), no. 6, 1038–1049. [11] B. Opozda and W. Mikulski, Cauchy-Kowalevski’s theorem applied for counting geometric structures, arxiv.org/abs/1605.06248v1. [12] B. Opozda and W. Mikulski, The Cauchy-Kowalevski theorem applied for counting connections with a prescribed Ricci tensor, Turk. J. Math. 42 (2018), 528–536. [13] E. Peyghan and L. Nourmohammadi Far, Foliations and a class of metrics on tangent bundle, Turk. J. Math. 37 (2013), 348–359. [14] C.R. Rao, Information and accuracy attainable in estimation of statistical parameters, Bull. Cal. Math. Soc. 37 (1945), 81–91. [15] A.A. Salimov and S. Kazimova, Geodesics of the Cheeger-Gromoll metric, Turk. J. Math. 33 (2009), 99–105. [16] S. Sasaki, On the differential geometry of tangent bundles of Riemannian manifolds, Tohoku Math. J. 10 (1958), 338–354. [17] K. Sun and S. Marchand-Maillet, An information geometry of statistical manifold learning, Proc. 31st Int. Conf. Machine Learn. (ICML-14), 2014, pp. 1–9. [18] F. Yildirim and A. Salimov, Semi-cotangent bundle and problems of lifts, Turk. J. Math. 38 (2014), 325–339. | ||
|
آمار تعداد مشاهده مقاله: 26,221 تعداد دریافت فایل اصل مقاله: 16,279 |
||