DOI QR코드

DOI QR Code

CHARACTERIZATIONS ON GEODESIC GCR-LIGHTLIKE SUBMANIFOLDS OF AN INDEFINITE KAEHLER STATISTICAL MANIFOLD

  • Received : 2022.03.10
  • Accepted : 2022.06.28
  • Published : 2022.09.01

Abstract

This article introduces the structure of GCR-lightlike submanifolds of an indefinite Kaehler statistical manifold and derives their geometric properties. The characterizations on totally geodesic, mixed geodesic, D-geodesic and D'-geodesic GCR-lightlike submanifolds have also been obtained.

Keywords

References

  1. S. Amari, Differential geometrical methods in statistics, Lecture Notes in Statistics 28 Springer, New York, 1985.
  2. S. Amari, Differential geometrical theory of statistics, Differential Geometry in Statistical Inference, Institute of Mathematical Statistics, Hayward, California 10 (1987), 19-94.
  3. K. L. Duggal and A. Bejancu, Light-like CR hypersurfaces of indefinite Kaehler manifolds, Acta Applicandae Mathematica 31 (1993), no. 2, 171-190. https://doi.org/10.1007/BF00990541
  4. K. L. Duggal, A. Bejancu, Lightlike submanifolds of semi-Riemannian manifolds and applications, Mathematics and its Applications 364, Kluwer Academic, 1996.
  5. K. L. Duggal and B. Sahin, Screen Cauchy Riemann lightlike submanifolds, Acta Math. Hungar. 106 (2005), no. 1-2, 137-165. https://doi.org/10.1007/s10474-005-0011-7
  6. K. L. Duggal and B. Sahin, Generalized Cauchy-Riemann lightlike submanifolds of Kaehler manifolds, Acta Math. Hungar. 112 (2006), no. 1-2, 107-130 . https://doi.org/10.1007/s10474-006-0068-y
  7. H. Furuhata, Hypersurfaces in statistical manifolds, Differential Geometry and its Applications 27 (2009), no. 3, 420-429. https://doi.org/10.1016/j.difgeo.2008.10.019
  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, Journal of Geometry and Physics 117 (2017), 179-186. https://doi.org/10.1016/j.geomphys.2017.03.010
  10. J. Kaur and V. Rani, Distributions in CR-lightlike submanifolds of an indefinite Kaehler statistical manifold, Malaya Journal of Matematik 8 (2020), no. 4, 1346-1353. https://doi.org/10.26637/MJM0804/0001
  11. R. Kumar, S. Kumar, and R. K. Nagaich, GCR-lightlike product of indefinite Kaehler manifolds, International Scholarly Research Notices 2011 (2011).
  12. S. Kumar, R. Kumar, and R. K. Nagaich, GCR-lightlike submanifolds of indefinite nearly Kaehler manifolds, Bulletin of the Korean Mathematical Society 50 (2013), no. 4, 1173-1192. https://doi.org/10.4134/BKMS.2013.50.4.1173
  13. T. Kurose, Geometry of statistical manifolds, Mathematics in the 21st Century, 34-43, 2004.
  14. M. Milijevic, Totally real statistical submanifolds, Interdisciplinary Information Sciences 21 (2015), no. 2, 87-96. https://doi.org/10.4036/iis.2015.87
  15. M. Milijevic, CR-submanifolds in holomorphic statistical manifolds, Ph.D Thesis in Science, Department of Mathematics, Graduates School of Science, Hokkaido University, 2015.
  16. T. Noda, Sympletic structures on statistical manifolds, Journal of the Australian Mathematical Society 90 (2011), no. 3, 371-384 . https://doi.org/10.1017/S1446788711001285
  17. V. Rani and J. Kaur, Cauchy Riemann-lightlike submanifolds in the aspect of an indefinite Kaehler statistical manifold, Malaya Journal of Matematik 9 (2021), no. 1, 136-143. https://doi.org/10.26637/MJM0901/0023
  18. V. Rani and J. Kaur, On structure of lightlike hypersurfaces of an indefinite Kaehler statistical manifold, Differential Geometry-Dynamical Systems 23 (2021), 221-234.
  19. C. R. Rao, Information and the accuracy attainable in the estimation of statistical parameters, Bulletin of Calcutta Mathematical Society 37 (1945), 81-91.
  20. B. Sahin and R. Gunes, Geodesic CR-lightlike submanifolds, Beitrage zur Algebra und Geometrie, Contribution to Algebra and Geometry 42 (2001), no. 2, 583-594.
  21. A. Yazla, I. K. Erken, and C. Murathan, Almost cosymplectic statistical manifolds, preprint (2018); arXiv:1801.09890.