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.
Gorodski, Topics in polar actions, preprint
2 Pith papers cite this work. Polarity classification is still indexing.
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Dual leaves of polar actions on simply connected complete nonnegatively curved manifolds are totally geodesic and closed, themselves polar and nonnegatively curved, inducing a Riemannian submersion to a homogeneous space.
citing papers explorer
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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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The dual foliation of polar actions on nonnegatively curved manifolds
Dual leaves of polar actions on simply connected complete nonnegatively curved manifolds are totally geodesic and closed, themselves polar and nonnegatively curved, inducing a Riemannian submersion to a homogeneous space.