Statistical manifolds with the same statistic and Riemann curvature tensor fields

Fereshteh Malek

doi:10.5269/bspm.71410

Fereshteh Malek K. N. TOOsi university of Technology

Abstract

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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