THERMAL SCIENCE

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Sema Kazan

ANTI-INVARIANT ξ⊥-COSYMPLECTIC-LIKE STATISTICAL SUBMERSIONS

ABSTRACT
Our purpose in this article is to study anti-invariant ξ⊥-cosymplectic-like statistical submersions from cosymplectic-like statistical manifolds and an example. Also, we investigate the integrability and the totally geodesicness of the distributions and the geometry of foliations.
KEYWORDS
Kahler-like statistical manifold, statistical submersion, cosymplectic-like statistical manifold, statistical manifold
PAPER SUBMITTED: 2021-06-19
PAPER REVISED: 2021-11-01
PAPER ACCEPTED: 2022-05-06
PUBLISHED ONLINE: 2022-07-23
DOI REFERENCE: https://doi.org/10.2298/TSCI2204991K
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2022, VOLUME 26, ISSUE Issue 4, PAGES [2991 - 3001]
REFERENCES
  1. Rao, C. R., Information and Accuracy Attainable in the Estimation of Statistical Parameters, Bulletin of the Calcutta Mathematical Society, 37 (1945), pp. 81-91
  2. Ay, N., Tuschmann, W., Dually Flat Manifolds and Global Information Geometry, Open Syst. and Information Dyn., 9 (2002), June, pp. 195-200
  3. Amari, S., Differential-Geometrical Methods in Statistics, Lecture Notes in Statistics, Springer, New York, USA, 1985, Vol. 28
  4. Blaga, A. M., Crasmareanu, M., Golden Statistical Structures (in Bulgarian), Comptes Rendus de l'Acad Emie Bulgare des Sciences, 69 (2016), 9, pp. 1113-1120
  5. Calin, O., Udriste, C., Geometric Modelling in Probability and Statistics, Springer, New York, USA, 2014
  6. Matsuzoe, H., et al, Equiaffine Structures on Statistical Manifolds and Bayesian Statistics, Differential Geometry and its Applications, 24 (2006), 6, pp, 567-578
  7. Noguchi, M., Geometry of Statistical Manifolds, Differential Geometry and its Applications, 2 (1992), 3, pp. 197-222
  8. Vilcu, A. D., Vilcu, G. E., Statistical Manifolds with Almost Quaternionic Structures and Quaternionic Kahler-Like Statistical Submersions, Entropy, 17 (2015), 9, pp. 6213-6228
  9. Furuhata, H., et al., Sasakian Statistical Manifolds, Journal of Geometry and Physics, 117 (2017), July, pp. 179-186
  10. Kazan, A., Conformally-Projectively Flat Trans-Sasakian Statistical Manifolds, Physica A: Statistical Mechanics and its Applications, 535 (2019), 122441
  11. Kazan, S., Kazan, A., Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection, Universal Journal of Mathematics and Applications, 1 (2018), 4, pp. 226-232
  12. Abe, N., Hasegawa, K., An Affine Submersion with Horizontal Distribution and Its Applications, Differential Geom. Appl., 14 (2001), 3, pp. 235-250
  13. O'Neill, B., Submersions and Geodesics, Duke Math. J., 34 (1967), pp. 363-373
  14. O'Neill, B., The Fundamental Equations of a Submersion, Michigan Math. J., 13 (1966), pp. 459-469
  15. Takano, K., Statistical Manifolds with Almost Complex Structures and Its Statistical Submersions, Tensor, N. S., 65 (2004), pp. 123-137
  16. Takano, K., Examples of the Statistical Submersion on the Statistical Model, Tensor, N. S., 65 (2004), pp. 170-178
  17. Takano, K., Statistical Manifolds with Almost Contact Structures and Its Statistical Submersions, Journal Geom., 85 (2006), Sept., pp. 171-187
  18. Vilcu, G. E., Almost Product Structures on Statistical Manifolds and Para-Kahler-Like Statistical Submersions, Bull. Sci. Math., 171 (2021), 103018
  19. Aytimur, H., Ozgur, C., On Cosymplectic-Like Statistical Submersions, Mediterr. J. Math., 16 (2019), 3, 70
  20. Siddiqui, A. N., et al., Chen Inequalities for Statistical Submersions between Statistical Manifolds, Int. J. Geom. Methods Mod. Phys., 18 (2021), 4, 2150049
  21. Watson, B., Almost Hermitian Submersions, Journal Differential Geometry, 11 (1976), 1, pp. 147-165
  22. Akyol, M. A., Gunduzalp, Y., On the Geometry of Conformal Anti-Invariant ξ⊥-Submersions, Int. J. Maps Math., 1 (2018), 1, pp. 50-67
  23. Lee, J. W., Anti-Invariant ξ⊥-Riemannian Submersions from Almost Contact Manifolds, Hacettepe Journal of Mathematics and Statistics, 42 (2013), 2, pp. 231-241
  24. Sahin, B., Anti-Invariant Riemannian Submersions from Almost Hermitian Manifolds, Cent. Eur. J. Math. 8, (2010) 3, pp. 437-447
  25. Siddiqi, M. D., Akyol, M. A., Anti-Invariant ξ⊥-Riemannian Submersions from Hyperbolic β-Kenmotsu Manifolds, Cubo, 20 (2018), 1, pp. 79-94
  26. Zhang, J., A Note on Curvature of α-Connections of a Statistical Manifold, Annals of the Institute of Statistical Mathematics, 59 (2007), pp. 161-170
  27. Murathan, C., Sahin, B., A Study of Wintgen Like Inequality for Submanifolds in Statistical Warped Product Manifolds, Journal Geom., 109 (2018), 2, 30
  28. O'Neill, B., Semi-Riemannian Geometry with Application Relativity, Academic Press, New York, USA, 1983
  29. Falcitelli, M., et al., Riemannian Submersions and Related Topics, World Scientific, River Edge, N. J., USA, 2004
  30. Altafini, C., Redundant Robotic Chains on Riemannian Submersions, IEEE Transactions on Robotics and Automation, 20 (2004), 2, pp. 335-340
  31. Sahin, B., Riemannian Submersions, Riemannian Maps in Hermitian Geometry, and Their Applications, Academic Press, Elsevier, Cambridge Mass. USA, 2017
  32. Le, H. V., Statistical Manifolds Are Statistical Models, Journal Geom., 84 (2005), Mar., pp. 83-93
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Anti-invariant ξ⊥-cosymplectic-like statistical submersions

© 2024 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence