Moduli spaces of left-invariant statistical structures are introduced and computed on three Lie groups with unique left-invariant metrics, yielding classifications of conjugate-symmetric and dually-flat structures.
In: Probabilistic Approach to Geometry vol
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Establishes geodesic connectedness from completeness for affine connections on statistical manifolds with divisible cubic forms, producing a Cartan-Hadamard theorem.
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The moduli spaces of left-invariant statistical structures on Lie groups
Moduli spaces of left-invariant statistical structures are introduced and computed on three Lie groups with unique left-invariant metrics, yielding classifications of conjugate-symmetric and dually-flat structures.
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Geodesic Connectedness on Statistical Manifolds with Divisible Cubic Forms
Establishes geodesic connectedness from completeness for affine connections on statistical manifolds with divisible cubic forms, producing a Cartan-Hadamard theorem.