Intrinsic four-point properties

Many characterizations of euclidean spaces (real inner product spaces) among metric spaces have been based on euclidean four point embeddability properties. Related “intrinsic” four point properties have also been used to characterize euclidean or hyperbolic spaces among a suitable class of metric spaces. The present paper provides new characterizations of euclidean or hyperbolic spaces based on intrinsic four point properties which are related to known four point embedding properties.