Geometry of the Fisher–Rao metric on the space of smooth densities on a compact manifold
Copyright policy )Geometry of the Fisher–Rao metric on the space of smooth densities on a compact manifold
AbstractIt is known that on a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive densities that is invariant under the action of the diffeomorphism group, is of the form urn:x-wiley:0025584X:media:mana201600523:mana201600523-math-0001for some smooth functions of the total volume . Here we determine the geodesics and the curvature of this metric and study geodesic and metric completeness.
- University of Vienna Austria
- Brunel University London United Kingdom
Manifolds of mappings, Mathematics - Differential Geometry, information geometry, Primary: 58B20, 101003 Applied geometry, space of densities, 58B20, 58D15, surfaces of revolution, 101032 Functional analysis, Fisher-Rao metric, Geodesics in global differential geometry, 101006 Differentialgeometrie, 58D15, 101006 Differential geometry, 101032 Funktionalanalysis, Differential Geometry (math.DG), 101003 Angewandte Geometrie, Fisher–Rao metric, FOS: Mathematics, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
Manifolds of mappings, Mathematics - Differential Geometry, information geometry, Primary: 58B20, 101003 Applied geometry, space of densities, 58B20, 58D15, surfaces of revolution, 101032 Functional analysis, Fisher-Rao metric, Geodesics in global differential geometry, 101006 Differentialgeometrie, 58D15, 101006 Differential geometry, 101032 Funktionalanalysis, Differential Geometry (math.DG), 101003 Angewandte Geometrie, Fisher–Rao metric, FOS: Mathematics, Riemannian, Finsler and other geometric structures on infinite-dimensional manifolds
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