Mappings preserving two hyperbolic distances

Link:

https://doi.org/10.1007/pl00000996

Autor/in:

Benz, Walter

Erscheinungsjahr:

2001

Medientyp:

Text

Schlagworte:

Article
Article

Beschreibung:

Suppose that X is the set of points of a hyperbolic geometry of finite or infinite dimension ≥ 2, and that ρ > 0 is a fixed real number and N > 1 a fixed integer. Let f : X > X be a mapping such that for every x,y ∈ X if h (x, y) = ρ, then h (f (x), f (y)) ≤ ρ and if h (x, y) = N ρ then h (f (x), f (y)) ≥ N ρ where h (p, q) designates the hyperbolic distance of p, q ∈ X. Then f is an isometry of X. Note that there is no regularity assumption on f, like continuity or even differentiability. Moreover, we present an example showing that the assumption that one fixed distance > 0 is preserved does not characterize hyperbolic isometries. © Birkhäuser Verlag, Basel, 2001.

Lizenz:

info:eu-repo/semantics/closedAccess

Quellsystem:

Forschungsinformationssystem der UHH

Interne Metadaten

Quelldatensatz: oai:www.edit.fis.uni-hamburg.de:publications/33208e58-8228-479d-b7cb-57bb30365967