Einstein metrics on mixed 3-structure statistical manifolds

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Zanjan, Zanjan, Iran

2 Department of Mathematics, University of Zanjan, Zanjan, Iran.

Abstract

This paper presents a comprehensive study of curvature properties on statistical manifolds endowed with mixed 3-Sasakian and mixed 3-cosymplectic structures. We derive necessary and sufficient conditions for mixed 3-Sasakian statistical manifolds to be Einstein, establishing fundamental identities for the Ricci tensor and scalar curvature. Furthermore, we introduce and analyze mixed 3-cosymplectic statistical manifolds, proving that they are necessarily Ricci-flat. The interplay between statistical duality and these geometric structures yields rich curvature constraints that are thoroughly analyzed. We provide explicit examples of both mixed 3-Sasakian Einstein and mixed 3-cosymplectic Ricci-flat statistical manifolds, discussing their physical implications in the context of general relativity and field theories. The results generalize previous work on Sasakian and cosymplectic geometry to the statistical setting, opening new paths for research in information geometry and theoretical physics.

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References

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Journal of Hyperstructures

Articles in Press, Accepted Manuscript
Available Online from 07 July 2026

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