TY - JOUR T1 - PARA META-GOLDEN STATISTICAL MANIFOLDS WITH DUAL-SEMI-CONJUGATE CONNECTION AU - Karakuş Bağci, Naime AU - Aktan, Nesip PY - 2025 DA - April Y2 - 2025 JF - Konuralp Journal of Mathematics JO - Konuralp J. Math. PB - Mehmet Zeki SARIKAYA WT - DergiPark SN - 2147-625X SP - 100 EP - 107 VL - 13 IS - 1 LA - en AB - 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. KW - Meta-Golden structure KW - statistical manifolds KW - conjugate connection CR - [1] Amari, S., Differential-geometrical Methods in statistics; Lecture Notes in Statistics, Springer-Verlag: New York, NY, USA, 28 (1985). CR - [2] Bartlett, C. Nautilus Spirals and the Meta-Golden Ratio Chi. Nexus Netw J., 21 (2019), 641–656 . CR - [3] Blaga, A.M. and Mircea, C., “Golden-Statistical Structures.” Comptes rendus de l’Academie bulgare des Sciences, 69 (2016), 1113-1120. CR - [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. CR - [5] Calin, O.; Matsuzoe, H.; Zhang J.; Generalizations of Conjugate Connections, Trends in Differential Geometry, Complex Analysis and Mathematical Physics, 2009. CR - [6] Crasmareanu M, Heratcanu CE., Golden Differential Geometry, Chaos Solitions Fractals, 38(5) (2008), 1229-1238. CR - [7] De, U.C.; Shaikh A.A., Differentil Geometry of Manifolds, Alpha Science International Ltd., Oxford, UK., 2007. CR - [8] Etayo F, Santamaria R, Upadhyay A. On the geometry of almost Golden Riemannian manifolds. Mediterranean J Math., 14(187) (2017). CR - [9] Furuhata, H., Hasegawa, I., Okuyama, Y. et al. Kenmotsu statistical manifolds and warped product. J. Geom., 108 (2017), 1175-1191. CR - [10] Furuhata, H., Hasegawa, I.,Okuyama, Y.,Sato, K., Shahidd, M.H., Sasakian statistical manifolds, Journal of Geometry and Physics, 117 (2017), 179-186. CR - [11] Gezer A, Cengiz N, Salimov A., On integrability of Golden Riemannian structures, Turkish J Math., 37 (2013), 693-703. CR - [12] Gherici B., S-Golden manifolds, Mediterr J Math., 16(56) (2019). CR - [13] Gherici B., A new class of Golden Riemannian manifold, Int. Elect. J. Geometry, 13 (2020), 1-8. CR - [14] Hretcanu CE, Crasmareanu M., Metallic structures on Riemannian manifolds. Rev Un Mat Argentina, 54 (2013), 15-27. CR - [15] Huylebrouck, D., The Meta-golden Ratio Chi, Mathematics, Music, Art, Architecture, Culture, (2014), 151-158. CR - [16] Karaman C., On metallic semi-symmetric metric F-connections. Commun Fac Sci Univ Ank S´er A1 Math Stat., 67 (2018), 242-251. CR - [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. CR - [18] Mclnerney, A., First Steps in differenatial Geometry, Springer, 2013. CR - [19] O˘guzhan B., Some ˙Inequalities for Statistical Submanifolds in Metallic-like Statistical Manifolds, Turk. J. Math. Comput. Sci., 13 (2012), 348-358. CR - [20] O¨ zkan M. Prolongations of golden structures to tangent bundles. Differential Geometry - Dyn Syst., 16 (2014), 227-238. CR - [21] O¨ zkan M, Peltek B. A new structure on manifolds: silver structure. Int Elect J Geometry, 9 (2016), 59-69. CR - [22] S¸ ahin F, S¸ ahin B., Meta-Golden Riemannian manifolds, Math Meth Appl Sci., 45 (2022), 10491-10501. CR - [23] Udris¸te, C., Calin, O., Geometric Modelling in Probabilty and Statistics, Springer Interntional Publishing Switzerlaand, 2014. CR - [24] Yildirim, M., Semi-symmetric non-metric connections on statistical manifolds, J. Geom. Phys. 176(2022), 104505. UR - https://dergipark.org.tr/en/pub/konuralpjournalmath/issue//1661603 L1 - https://dergipark.org.tr/en/download/article-file/4707517 ER -