
AIMS Mathematics, 2020, 5(4): 34953509. doi: 10.3934/math.2020227.
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On Ricci curvature of submanifolds in statistical manifolds of constant (quasiconstant) curvature
1 Department of Mathematics, Jamia Millia Islamia, New Delhi110025, India
2 Department of Mathematics Education and RINS, Gyeongsang National University, Jinju 52828, Republic of Korea
Received: , Accepted: , Published:
Keywords: statistical manifolds; quasiconstant curvature; Ricci curvature; ChenRicci inequality; statistical immersion
Citation: Aliya Naaz Siddiqui, Mohammad Hasan Shahid, Jae Won Lee. On Ricci curvature of submanifolds in statistical manifolds of constant (quasiconstant) curvature. AIMS Mathematics, 2020, 5(4): 34953509. doi: 10.3934/math.2020227
References:
 1. B. Y. Chen, Relationship between Ricci curvature and shape operator for submanifolds with arbitrary codimensions, Glasgow Math. J., 41 (1999), 3341.
 2. B. Y. Chen, Some pinching and classification theorems for minimal submanifolds, Arch. Math., 6 (1993), 568578.
 3. A. Mihai, I. Mihai, Curvature invariants for statistical submanifolds of hessian manifolds of constant hessian curvature, Mathematics, 6 (2018), 44.
 4. A. N. Siddiqui, Y. J. Suh, O. Bahadir, Extremities for statistical submanifolds in Kenmotsu statistical manifolds, 2019.
 5. S. Amari, DifferentialGeometrical methods in statistics, lecture notes in statistics, Springer: New York, NY, USA, 1985.
 6. P. W. Vos, Fundamental equations for statistical submanifolds with applications to the Bartlett correction, Ann. Inst. Stat. Math., 41 (1989), 429450.
 7. H. Furuhata, Hypersurfaces in statistical manifolds, Differ. Geom. Appl., 67 (2009), 420429.
 8. B. Opozda, Bochner's technique for statistical structures, Ann. Global Anal. Geom., 48 (2015), 357395.
 9. B. Opozda, A sectional curvature for statistical structures, Linear Algebra Appl., 497 (2016), 134161.
 10. M. E. Aydin, A. Mihai, I. Mihai, Some inequalities on submanifolds in statistical manifolds of constant curvature, Filomat, 29 (2015), 465477.
 11. H. Aytimur, C. Ozgur, Inequalities for submanifolds in statistical manifolds of quasiconstant curvature, Ann. Polonici Mathematici, 121 (2018), 197215.
 12. T. Oprea, On a geometric inequality, arXiv:math/0511088v1[math.DG], 2005.
 13. T. Oprea, Optimizations on riemannian submanifolds, An. Univ. Bucureşti Mat., 54 (2005), 127136.
 14. L. Peng, Z. Zhang, Statistical Einstein manifolds of exponential families with groupinvariant potential functions, J. Math. Anal. and App., 479 (2019), 21042118.
 15. A. Rylov, Constant curvature connections on statistical models, In: Ay N., Gibilisco P., Matúš F. Information geometry and its applications. IGAIA IV 2016. Eds. Springer Proceedings in Mathematics Statistics, Springer, Cham, 252 (2018), 349361.
 16. K. Arwini, C. T. J. Dodson, Information geometry: Near randomness and near independence, lecture notes in mathematics, SpringerVerlag Berlin Heidelberg, 1953 (2008), 260.
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