The horofunction boundary of the infinite dimensional hyperbolic space. (English) Zbl 1442.51005
Let \((H , \langle, \cdot,\rangle)\) be an infinite-dimensional Hilbert space and let \(V = {\mathbb R}\oplus H\). The point set of Klein’s model of the infinite-dimensional real hyperbolic space \({\mathbb H}^{\infty}\) consists of all \((1, x)\in V\) with \(\|x\|<1\), equipped with Hilbert’s cross-ratio metric. In this paper, the author determines the horofunctions of \({\mathbb H}^{\infty}\) as well as the Busemann points among them.
Reviewer: Victor V. Pambuccian (Glendale)
MSC:
| 51M10 | Hyperbolic and elliptic geometries (general) and generalizations |
| 53C23 | Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces |
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