Fisher information geometry, Poisson kernel and asymptotical harmonicity
| Autor: | Hiroyasu Satoh, Mitsuhiro Itoh |
|---|---|
| Rok vydání: | 2011 |
| Předmět: |
Poisson kernel
Hadamard manifold Geometry Rank (differential topology) Fisher information metric Statistical manifold Homothetic transformation symbols.namesake Computational Theory and Mathematics Asymptotically harmonic Symmetric space Busemann function symbols Visibility Mathematics::Differential Geometry Geometry and Topology Analysis Mathematics |
| Zdroj: | Differential Geometry and its Applications. 29:S107-S115 |
| ISSN: | 0926-2245 |
| Popis: | Let ( X , g ) be an Hadamard manifold with ideal boundary ∂X. We can then define the map φ : X → P ( ∂ X ) associated with Poisson kernel on X, where P ( ∂ X ) is the space of probability measures on ∂X, together with the Fisher information metric G. We make geometrical investigation of homothetic property and minimality of this map with respect to the metrics g and G. The map φ is shown to be a minimal homothetic embedding for a rank one symmetric space of noncompact type as well as for a nonsymmetric Damek–Ricci space. The following is also obtained. If φ is assumed to be homothetic and minimal, then, ( X , g ) turns out to be an asymptotically harmonic, visibility manifold with the Poisson kernel being expressed in terms of the Busemann function. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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