STATISTICAL MANIFOLDS WITH THE SAME STATISTIC AND RIEMANN CURVATURE TENSOR FIELDS
Resumen
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.
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Citas
[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, Birkhäuser, 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, Birkhäuser, 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.
Publicado
2025-07-13
Número
Sección
Research Articles
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
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