Strong additivity of metric isosceles orthogonality (Q1266489)

The authors give two characterizations of euclidean and hyperbolic spaces: Firstly, those spaces are exactly the complete, convex, and externally convex metric spaces which satisfy the property that metric isosceles orthogonality is strongly additive. Secondly, one may characterize those spaces as being finitely compact, convex, and externally convex metric spaces with a unique metric line through any two points which satisfy that metric isosceles orthogonality is additive.