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Einstein metrics on mixed 3-structure statistical manifolds | ||
| Journal of Hyperstructures | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 16 تیر 1405 اصل مقاله (1.62 M) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22098/jhs.2026.18615.1147 | ||
| نویسندگان | ||
| Soheil Najd Ghiorbani1؛ Mohammad Bagher Kazemi Balgeshir* 2 | ||
| 1Department of Mathematics, University of Zanjan, Zanjan, Iran | ||
| 2Department of Mathematics, University of Zanjan, Zanjan, Iran. | ||
| چکیده | ||
| This paper presents a comprehensive study of curvature properties on statistical manifolds endowed with mixed 3-Sasakian and mixed 3-cosymplectic structures. We derive necessary and sufficient conditions for mixed 3-Sasakian statistical manifolds to be Einstein, establishing fundamental identities for the Ricci tensor and scalar curvature. Furthermore, we introduce and analyze mixed 3-cosymplectic statistical manifolds, proving that they are necessarily Ricci-flat. The interplay between statistical duality and these geometric structures yields rich curvature constraints that are thoroughly analyzed. We provide explicit examples of both mixed 3-Sasakian Einstein and mixed 3-cosymplectic Ricci-flat statistical manifolds, discussing their physical implications in the context of general relativity and field theories. The results generalize previous work on Sasakian and cosymplectic geometry to the statistical setting, opening new paths for research in information geometry and theoretical physics. | ||
| کلیدواژهها | ||
| Statistical 3-structure؛ Einstein manifolds؛ mixed 3-Sasakian | ||
| مراجع | ||
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[1] S. Amari and H. Nagaoka, Methods of Information Geometry, Amer. Math. Soc., 2000. [2] F. Asali, M.B. Kazemi Balgeshir, On statistical generalized recurrent manifolds, Journal of Finsler Geometry and its Applications 29(2) (2024), 101-115. [3] A. L. Besse, Einstein Manifolds, Springer, 2008. [4] C. P. Boyer and K. Galicki, On Sasakian-Einstein geometry, Internat. J. Math. 11 (2000), 873–909. [5] A. Caldarella, A.M. Pastore, Mixed 3-Sasakian structures and curvature, Ann. Polon. Math. 96 (2009) 107–125. [6] H. Furuhata, I. Hasegawa, Y. Okuyama, K. Sato and M. H. Shahid, Sasakian statistical manifolds, J. Geom. Phys. 117, 180–192, 2017. [7] S. Ianus, L. Ornea and G. E. Vilcu, Submanifolds in manifolds with metric mixed 3-structures, Mediterr. J. Math. 9 (2012), 105–130. [8] M. B. Kazemi Balgeshir, On submanifolds of Sasakian statistical manifolds, Boletim Da Sociedade Paranaense De Matem´atica, 40 (2021), 1-6. https://doi.org/10.5269/bspm.42402 [9] Y. Kuo, On almost contact 3-structure, Tohoku Math. J. 22 (1970), 325–332. [10] S. L. Lauritzen, Statistical manifolds, IMS Lecture Notes-Monograph Series 10, 163–216, 1987. [11] J. Majidi, A. Tayebi, A. Haji-Badali, On Einstein-reversible mth root Finsler metrics, Inter. J. Geom. Meth. Modern Phys. 20(6) (2023), 235009. [12] F. Malek, M.B. Kazemi Balgeshir, Semi-slant and bi-slant submanifolds of almost contact metric 3-structure manifolds, Turkish J. Math. 37(6) (2013), 1030–1039. [13] S. Sasaki, On differentiable manifolds with certain structures which are closely related to almost contact structure, Tohoku Math. J. 12 (1960), 459–476. [14] M. Vasiulla, M. Ali, I. ¨Unal, A study of mixed super quasi-Einstein manifolds with applications to general relativity, Inter. J. Geom. Meth. Modern Phys. 21 (2024), 2450177. | ||
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