# Straight projective-metric spaces with centers

## TL;DR

This paper characterizes straight projective-metric spaces with centers, showing they are either hyperbolic or Minkowskian geometries, based on the distribution and number of centers present.

## Contribution

It provides a complete characterization of straight projective-metric spaces with centers, linking their structure to hyperbolic and Minkowskian geometries.

## Key findings

- Spaces with an open set of centers are hyperbolic or Minkowskian.
- Spaces with finitely many well-placed centers are hyperbolic or Minkowskian.
- Centers characterize the geometry of straight projective-metric spaces.

## Abstract

It is proved that a straight projective-metric space has an open set of centers, if and only if it is either the hyperbolic or a Minkowskian geometry. It is also shown that if a straight projective-metric space has some finitely many well-placed centers, then it is either the hyperbolic or a Minkowskian geometry.