Statistical manifolds with the same statistic and Riemann curvature tensor fields
DOI:
https://doi.org/10.5269/bspm.71410Resumo
This paper provides a necessary and sufficient condition for an almost contact metric statistical manifold to have the same statistic and Riemann curvature tensor fields, and a condition to determine the uniqueness of such a statistical structures. Additionally, we prove that a contact metric statistical manifold in which the integral curves of the Reeb vector field are geodesics, is a trivial statistical manifold if and only if it has the same statistic and Riemann curvature tensor fields.
Referências
1. H. Akbari and F. Malek, On contact metric statistical manifolds, Differ. Geom. Appl., 75 (2021), 1-16.
2. H. Akbari and F. Malek, On the Hypersurfaces of Almost Hermitian Statistical Manifolds, Bulletin of the Iranian Mathematical Society, 48 (2022), 2669–2684.
3. S. Amari, Differential-geometrical methods in statistics. Lecture Notes in Statistics, Springer-Verlag, New York, (1985).
4. S. Amari, H. Nagaoka, Methods of Information Geometry, American Mathematical Soc., 191, (2007).
5. D. E. Blair, Riemannian geometry of contact and symplectic manifold, (Second edition), Progress in Math. 203, Birkhauser, Boston, (2010).
6. H. Furuhata, Hypersurfaces in statistical manifolds, Differential Geom. Appl. 27 (3), (2009), 420–429.
7. H. Furuhata, I. Hasegawa, Submanifolds theory in holomorphic statistical manifolds, Geometry of Cauchy-Riemann submanifolds, Springer, Singapore (2016), 179–215.
8. H. Furuhata, I. Hasegawa, Y. Okuyama and K. Sato, Kenmotsu statistical manifolds and warped product, J. Geom., 108 (3), (2017), 1175–1191.
9. H. Furuhata, I. Hasegawa, Y. Okuyama, K. Sato and M. H. Shahid, Sasakian statistictical manifolds, J. Geom. Phys. 117, (2017), 179—186.
2. H. Akbari and F. Malek, On the Hypersurfaces of Almost Hermitian Statistical Manifolds, Bulletin of the Iranian Mathematical Society, 48 (2022), 2669–2684.
3. S. Amari, Differential-geometrical methods in statistics. Lecture Notes in Statistics, Springer-Verlag, New York, (1985).
4. S. Amari, H. Nagaoka, Methods of Information Geometry, American Mathematical Soc., 191, (2007).
5. D. E. Blair, Riemannian geometry of contact and symplectic manifold, (Second edition), Progress in Math. 203, Birkhauser, Boston, (2010).
6. H. Furuhata, Hypersurfaces in statistical manifolds, Differential Geom. Appl. 27 (3), (2009), 420–429.
7. H. Furuhata, I. Hasegawa, Submanifolds theory in holomorphic statistical manifolds, Geometry of Cauchy-Riemann submanifolds, Springer, Singapore (2016), 179–215.
8. H. Furuhata, I. Hasegawa, Y. Okuyama and K. Sato, Kenmotsu statistical manifolds and warped product, J. Geom., 108 (3), (2017), 1175–1191.
9. H. Furuhata, I. Hasegawa, Y. Okuyama, K. Sato and M. H. Shahid, Sasakian statistictical manifolds, J. Geom. Phys. 117, (2017), 179—186.
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Publicado
2025-07-13
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Como Citar
Malek, F. (2025). Statistical manifolds with the same statistic and Riemann curvature tensor fields. Boletim Da Sociedade Paranaense De Matemática, 43, 1-6. https://doi.org/10.5269/bspm.71410
