호남수학학술지 (Honam Mathematical Journal)

  • 제46권2호
  • /
  • Pages.224-236
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  • 2024
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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CR-PRODUCT OF A HOLOMORPHIC STATISTICAL MANIFOLD

  • Vandana Gupta (Department of Mathematics, PMN College) ;
  • Jasleen Kaur (Department of Mathematics, Punjabi University)
  • 투고 : 2023.07.08
  • 심사 : 2023.12.29
  • 발행 : 2024.06.25
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초록

This study inspects the structure of CR-product of a holomorphic statistical manifold. Findings concerning geodesic submanifolds and totally geodesic foliations in the context of dual connections have been demonstrated. The integrability of distributions in CR-statistical submanifolds has been characterized. The statistical version of CR-product in the holomorphic statistical manifold has been researched. Additionally, some assertions for curvature tensor field of the holomorphic statistical manifold have been substantiated.

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참고문헌

  1. S. Amari, Differential geometrical methods in statistics, Lect Notes Stat 28, Springer, New York, 1985.
  2. S. Amari, Differential geometrical theory of statistics, Differential Geometry in Statistical Inference 10 (1987), 19-94.
  3. A. Bejancu, CR-submanifolds of a Kaehler manifold I, Proc Am Math Soc 69 (1978), no. 1, 135-142.
  4. A. Bejancu, CR submanifolds of a Kaehler manifold II, Trans. Am. Math. Soc. 250 (1979), 333-345.
  5. A. Bejancu, Geometry of CR-submanifolds, Math. Appl., Springer Dordrecht, Holland 23, 1986.
  6. B. Y. Chen, CR-submanifolds of a Kaehler manifold I, J. Differ. Geom. 16 (1981), no. 2, 305-322.
  7. H. Furuhata, Hypersurfaces in statistical manifolds, Differ. Geom. Appl. 27 (2009), no. 3, 420-429.
  8. H. Furuhata and I. Hasegawa, Submanifold theory in holomorphic statistical manifolds, Geometry of Cauchy-Riemann Submanifolds, 179-215, Springer, Singapore, 2016.
  9. H. Furuhata, I. Hasegawa, Y. Okuyama, K. Sato, and M. H. Shahid, Sasakian statistical manifolds, J. Geom. Phys. 117 (2017), 179-186.
  10. T. Kurose, Geometry of statistical manifolds, Mathematics in the 21st Century, (2004), 34-43.
  11. M. Milijevic, Totally real statistical submanifolds, Interdiscip. Inf. Sci. 21 (2015), no. 2, 87-96.
  12. M. Milijevic, CR submanifolds in holomorphic statistical manifold, Ph.D Thesis in Science, Department of Mathematics Graduates School of Science, Hokkaido University, 2015.
  13. C. R. Rao, Information and the accuracy attainable in the estimation of statistical parameters, Bull Calcutta Math Soc 37 (1945), 81-91.
  14. A. N. Siddiqui and M. H. Shahid, On totally real statistical submanifolds, Filomat 32 (2018), no. 13, 4473-4483.
  15. A. N. Siddiqui, F. R. AL-Solamy, M. H. Shahid, and I. Mihai, On CR-statistical submanifolds of holomorphic statistical manifolds, Filomat 35 (2021), no. 11, 3571-3584.
  16. U. Simon, Affine differential geometry, In Handbook of differential geometry, Elsevier 1 (2000), 905-961.
  17. P. W. Vos, Fundamental equations for statistical submanifolds with applications to the Bartlett correction, Ann Inst Stat Math 41 (1989), no. 3, 429-450.
  18. K. Yano, and M. Kon, Structures on Manifolds, World Scientific, Singapore, Series in Pure Mathematics 3, 1984.
  19. A. Yazla, I. K. Erken, and C. Murathan, Almost cosymplectic statistical manifolds, preprint (2018) ; arXiv:1801.09890.