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Some Characterizations of PS-Statistical Manifolds

Yıl 2022, Cilt: 7 Sayı: 2, 116 - 131, 30.09.2022

Öz

In the present study, firstly we state symmetry properties for curvatures of a statistical manifold and give some relations between the Riemannian curvature b R and the curvatures R; R∗ and RS. After, by defining the notion of para-Sasakian statistical manifold, we give the necessary and sufficient conditions for a structure (D; h; Ψ; w; ζ) to be a para-Sasakian structure when (D; h) is a statistical structure and (Ψ; w; ζ; h) is an almost paracontact Riemannian manifold. Also, we give some results for curvatures R; R∗; RS and Ricci tensor of these curvatures on a para-Sasakian statistical manifold. We construct an example of para-Sasakian statistical manifold of dimension 3. Finally, we examined the Einsteinian of para-Sasakian statistical manifolds according to certain conditions.

Kaynakça

  • [1] T. Adati and K. Matsumoto; On Conformally Recurrent and Conformally Symmetric P-Sasakian Manifold, TRU Math., 13, 25-32, 1977.
  • [2] S. Amari; Differential-Geometrical Methods in Statistics, Lecture Notes in Statistics, 28, Springer, New York, 1985.
  • [3] A.M. Blaga and M. Crasmareanu; Golden Statistical Structures, Comptes rendus de l’Acad emie bulgare des Sciences, 69(9), 1113-1120, 2016.
  • [4] A. Bravetti and C. S. Lopez-Monsalvo; Para-Sasakian geometry in thermodynamic fluctuation theory, Journal of Physics A Mathematical and General 48:125206, DOI: 10.1088/1751-8113/48/12/125206, 2015.
  • [5] O. Calin and C. Udris¸te; Geometric Modeling in Probability and Statistics, Springer, 2014.
  • [6] H. Furuhata; Hypersurfaces in Statistical Manifolds, Differential Geometry and its Applications, 27, 420-429, 2009.
  • [7] H. Furuhata, I. Hasegawa, Y. Okuyama, K. Sato and M.H. Shahid; Sasakian Statistical Manifolds, Journal of Geometry and Physics, 117, 179-186, 2017.
  • [8] H. Furuhata, I. Hasegawa, Y. Okuyama and K. Sato; Kenmotsu Statistical Manifolds and Warped Product, J. Geom., DOI 10.1007/s00022-017-0403-1, 2017.
  • [9] A. Kazan; Conformally-Projectively Trans-Sasakian Statistical Manifolds, Physica A: Statistical Mechanics and its Applications, 535, 122441, DOI: https://doi.org/10.1016/j.physa.2019.122441, 2019.
  • [10] T. Kurose; Dual Connections and Affine Geometry, Math. Z., 203, 115-121, 1990.
  • [11] H. Matsuzoe, J-I. Takeuchi and S-I. Amari; Equiaffine Structures on Statistical Manifolds and Bayesian Statistics, Differential Geometry and its Applications, 24, 567–578, 2006.
  • [12] M. Noguchi; Geometry of Statistical Sanifolds, Differential Geometry and its Applications, 2, 197-222, 1992.
  • [13] C.R. Rao; Information and Accuracy Attainable in the Estimation of Statistical Parameters, Bulletin of the Calcutta Mathematical Society, 37, 81–91, 1945.
  • [14] S. Sasaki; On Differentiable Manifolds with Certain Structures which are Closely Related to Almost Contact Structure. I, The Tohoku Mathematical Journal. Second Series, vol. 12, 459–476, 1960.
  • [15] I. Sato; On a Structure Similar to the Almost Contact Structure, Tensor New Series, vol. 30, no. 3, pp. 219–224, 1976.
  • [16] S.S. Shukla and M.K. Shukla; On Ψ-Symmetric Para-Sasakian Manifolds, Int. Journal of Math. Analysis, 4(16), 761-769, 2010.
  • [17] S. Kazan and A. Kazan; Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection, Universal Journal of Mathematics and Applications, 1(4), 226-232, 2018.
  • [18] K. Takano; Statistical manifolds with Almost Complex Structures and its Statistical Submersions, Tensor N.S., 65, 128–142, 2004.
  • [19] K. Takano; Statistical Manifolds with Almost Contact Structures and its Statistical Submersions, Journal of Geometry, 85, 171-187, 2006.
  • [20] A-D. Vilcu and G-E. Vilcu; Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kahler-like Statistical Submersions, Entropy, 17, 6213-6228, 2015.
  • [21] J. Zhang; A Note on Curvature of α-Connections of a Statistical Manifold, Annals of the Institute of Statistical Mathematics, 59, 161-170, 2007.
Yıl 2022, Cilt: 7 Sayı: 2, 116 - 131, 30.09.2022

Öz

Kaynakça

  • [1] T. Adati and K. Matsumoto; On Conformally Recurrent and Conformally Symmetric P-Sasakian Manifold, TRU Math., 13, 25-32, 1977.
  • [2] S. Amari; Differential-Geometrical Methods in Statistics, Lecture Notes in Statistics, 28, Springer, New York, 1985.
  • [3] A.M. Blaga and M. Crasmareanu; Golden Statistical Structures, Comptes rendus de l’Acad emie bulgare des Sciences, 69(9), 1113-1120, 2016.
  • [4] A. Bravetti and C. S. Lopez-Monsalvo; Para-Sasakian geometry in thermodynamic fluctuation theory, Journal of Physics A Mathematical and General 48:125206, DOI: 10.1088/1751-8113/48/12/125206, 2015.
  • [5] O. Calin and C. Udris¸te; Geometric Modeling in Probability and Statistics, Springer, 2014.
  • [6] H. Furuhata; Hypersurfaces in Statistical Manifolds, Differential Geometry and its Applications, 27, 420-429, 2009.
  • [7] H. Furuhata, I. Hasegawa, Y. Okuyama, K. Sato and M.H. Shahid; Sasakian Statistical Manifolds, Journal of Geometry and Physics, 117, 179-186, 2017.
  • [8] H. Furuhata, I. Hasegawa, Y. Okuyama and K. Sato; Kenmotsu Statistical Manifolds and Warped Product, J. Geom., DOI 10.1007/s00022-017-0403-1, 2017.
  • [9] A. Kazan; Conformally-Projectively Trans-Sasakian Statistical Manifolds, Physica A: Statistical Mechanics and its Applications, 535, 122441, DOI: https://doi.org/10.1016/j.physa.2019.122441, 2019.
  • [10] T. Kurose; Dual Connections and Affine Geometry, Math. Z., 203, 115-121, 1990.
  • [11] H. Matsuzoe, J-I. Takeuchi and S-I. Amari; Equiaffine Structures on Statistical Manifolds and Bayesian Statistics, Differential Geometry and its Applications, 24, 567–578, 2006.
  • [12] M. Noguchi; Geometry of Statistical Sanifolds, Differential Geometry and its Applications, 2, 197-222, 1992.
  • [13] C.R. Rao; Information and Accuracy Attainable in the Estimation of Statistical Parameters, Bulletin of the Calcutta Mathematical Society, 37, 81–91, 1945.
  • [14] S. Sasaki; On Differentiable Manifolds with Certain Structures which are Closely Related to Almost Contact Structure. I, The Tohoku Mathematical Journal. Second Series, vol. 12, 459–476, 1960.
  • [15] I. Sato; On a Structure Similar to the Almost Contact Structure, Tensor New Series, vol. 30, no. 3, pp. 219–224, 1976.
  • [16] S.S. Shukla and M.K. Shukla; On Ψ-Symmetric Para-Sasakian Manifolds, Int. Journal of Math. Analysis, 4(16), 761-769, 2010.
  • [17] S. Kazan and A. Kazan; Sasakian Statistical Manifolds with Semi-Symmetric Metric Connection, Universal Journal of Mathematics and Applications, 1(4), 226-232, 2018.
  • [18] K. Takano; Statistical manifolds with Almost Complex Structures and its Statistical Submersions, Tensor N.S., 65, 128–142, 2004.
  • [19] K. Takano; Statistical Manifolds with Almost Contact Structures and its Statistical Submersions, Journal of Geometry, 85, 171-187, 2006.
  • [20] A-D. Vilcu and G-E. Vilcu; Statistical Manifolds with almost Quaternionic Structures and Quaternionic Kahler-like Statistical Submersions, Entropy, 17, 6213-6228, 2015.
  • [21] J. Zhang; A Note on Curvature of α-Connections of a Statistical Manifold, Annals of the Institute of Statistical Mathematics, 59, 161-170, 2007.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Volume VII Issue II
Yazarlar

Sema Kazan 0000-0002-8771-9506

Yayımlanma Tarihi 30 Eylül 2022
Yayımlandığı Sayı Yıl 2022 Cilt: 7 Sayı: 2

Kaynak Göster

APA Kazan, S. (2022). Some Characterizations of PS-Statistical Manifolds. Turkish Journal of Science, 7(2), 116-131.
AMA Kazan S. Some Characterizations of PS-Statistical Manifolds. TJOS. Eylül 2022;7(2):116-131.
Chicago Kazan, Sema. “Some Characterizations of PS-Statistical Manifolds”. Turkish Journal of Science 7, sy. 2 (Eylül 2022): 116-31.
EndNote Kazan S (01 Eylül 2022) Some Characterizations of PS-Statistical Manifolds. Turkish Journal of Science 7 2 116–131.
IEEE S. Kazan, “Some Characterizations of PS-Statistical Manifolds”, TJOS, c. 7, sy. 2, ss. 116–131, 2022.
ISNAD Kazan, Sema. “Some Characterizations of PS-Statistical Manifolds”. Turkish Journal of Science 7/2 (Eylül 2022), 116-131.
JAMA Kazan S. Some Characterizations of PS-Statistical Manifolds. TJOS. 2022;7:116–131.
MLA Kazan, Sema. “Some Characterizations of PS-Statistical Manifolds”. Turkish Journal of Science, c. 7, sy. 2, 2022, ss. 116-31.
Vancouver Kazan S. Some Characterizations of PS-Statistical Manifolds. TJOS. 2022;7(2):116-31.