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arXiv · 2609.34601

Determination of all diffeomorphism invariant tensor fields on the space of smooth positive densities on a compact manifold with corners

Peter W. Michor
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Abstract

It was proved in [3] that on a closed manifold of dimension greater than one, every smooth weak Riemannian metric on the space of smooth positive probability densities, that is invariant under the action of the diffeomorphism group, is a multiple of the Fisher-Rao metric. Here we extend this result to compact manifolds with corners, and we determine all diffeomorphism invariant tensor fields on the space of smooth positive probability densities.

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Peter W. Michor. 2026-09-28. Determination of all diffeomorphism invariant tensor fields on the space of smooth positive densities on a compact manifold with corners. https://arxiv.org/abs/2609.34601

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