期刊
MATHEMATISCHE NACHRICHTEN
卷 292, 期 3, 页码 511-523出版社
WILEY-V C H VERLAG GMBH
DOI: 10.1002/mana.201600523
关键词
Fisher-Rao metric; information geometry; space of densities; surfaces of revolution
类别
资金
- BRIEF award from Brunel University London
It 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 G(mu)(alpha, beta) = C-1 (mu(M)) integral(M) alpha/mu beta/mu mu + C-2 (mu(M)) integral(M) alpha . (integral M) beta for some smooth functions C-1, C-2 of the total volume mu(M). Here we determine the geodesics and the curvature of this metric and study geodesic and metric completeness.
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