发表机构
Universität Wien（维也纳大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将闭流形上Fisher-Rao度量唯一性定理推广至紧致带角流形，并完整刻画了正概率密度空间上的所有微分同胚不变张量场。
AI 中文摘要
在文献[3]中已证明，对于维数大于一的闭流形，光滑正概率密度空间上任意光滑弱黎曼度量，若在微分同胚群作用下不变，则必为Fisher-Rao度量的倍数。本文将这一结果推广到紧致带角流形，并确定了光滑正概率密度空间上的所有微分同胚不变张量场。
英文摘要
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.
Comments16 pages
