PARA META-GOLDEN STATISTICAL MANIFOLDS WITH DUAL-SEMI-CONJUGATE CONNECTION
Year 2025,
Volume: 13 Issue: 1, 100 - 107, 30.04.2025
Naime Karakuş Bağci
,
Nesip Aktan
Abstract
In this paper, a new class of statistical manifolds, referred to as meta-golden statistical manifolds, is defined, and the geometry of these mani- folds which have the dual-semi-conjugate connection is examined.
References
- [1] Amari, S., Differential-geometrical Methods in statistics; Lecture Notes in Statistics, Springer-Verlag: New York, NY, USA, 28 (1985).
- [2] Bartlett, C. Nautilus Spirals and the Meta-Golden Ratio Chi. Nexus Netw J., 21 (2019), 641–656 .
- [3] Blaga, A.M. and Mircea, C., “Golden-Statistical Structures.” Comptes rendus de l’Academie bulgare des Sciences, 69 (2016), 1113-1120.
- [4] Blaga, A. M. and Crasmareanu, M., The geometry of product conjugate connections. An. Stiint. Univ. Al. I. Cuza Iasi. Mat.(NS), 59(1) (2013), 73-84.
- [5] Calin, O.; Matsuzoe, H.; Zhang J.; Generalizations of Conjugate Connections, Trends in Differential Geometry, Complex Analysis and Mathematical
Physics, 2009.
- [6] Crasmareanu M, Heratcanu CE., Golden Differential Geometry, Chaos Solitions Fractals, 38(5) (2008), 1229-1238.
- [7] De, U.C.; Shaikh A.A., Differentil Geometry of Manifolds, Alpha Science International Ltd., Oxford, UK., 2007.
- [8] Etayo F, Santamaria R, Upadhyay A. On the geometry of almost Golden Riemannian manifolds. Mediterranean J Math., 14(187) (2017).
- [9] Furuhata, H., Hasegawa, I., Okuyama, Y. et al. Kenmotsu statistical manifolds and warped product. J. Geom., 108 (2017), 1175-1191.
- [10] Furuhata, H., Hasegawa, I.,Okuyama, Y.,Sato, K., Shahidd, M.H., Sasakian statistical manifolds, Journal of Geometry and Physics, 117 (2017), 179-186.
- [11] Gezer A, Cengiz N, Salimov A., On integrability of Golden Riemannian structures, Turkish J Math., 37 (2013), 693-703.
- [12] Gherici B., S-Golden manifolds, Mediterr J Math., 16(56) (2019).
- [13] Gherici B., A new class of Golden Riemannian manifold, Int. Elect. J. Geometry, 13 (2020), 1-8.
- [14] Hretcanu CE, Crasmareanu M., Metallic structures on Riemannian manifolds. Rev Un Mat Argentina, 54 (2013), 15-27.
- [15] Huylebrouck, D., The Meta-golden Ratio Chi, Mathematics, Music, Art, Architecture, Culture, (2014), 151-158.
- [16] Karaman C., On metallic semi-symmetric metric F-connections. Commun Fac Sci Univ Ank S´er A1 Math Stat., 67 (2018), 242-251.
- [17] Lone, M., Bahadir, O., Park, C. & Hwang, I.. Basic inequalities for statistical submanifolds in Golden-like statistical manifolds. Open Mathematics,
20 (2022), 153- 166.
- [18] Mclnerney, A., First Steps in differenatial Geometry, Springer, 2013.
- [19] O˘guzhan B., Some ˙Inequalities for Statistical Submanifolds in Metallic-like Statistical Manifolds, Turk. J. Math. Comput. Sci., 13 (2012), 348-358.
- [20] O¨ zkan M. Prolongations of golden structures to tangent bundles. Differential Geometry - Dyn Syst., 16 (2014), 227-238.
- [21] O¨ zkan M, Peltek B. A new structure on manifolds: silver structure. Int Elect J Geometry, 9 (2016), 59-69.
- [22] S¸ ahin F, S¸ ahin B., Meta-Golden Riemannian manifolds, Math Meth Appl Sci., 45 (2022), 10491-10501.
- [23] Udris¸te, C., Calin, O., Geometric Modelling in Probabilty and Statistics, Springer Interntional Publishing Switzerlaand, 2014.
- [24] Yildirim, M., Semi-symmetric non-metric connections on statistical manifolds, J. Geom. Phys. 176(2022), 104505.