Altitude properties and characterizations of inner product spaces (Q1841854)

The authors show that under certain conditions a complete, convex, externally convex metric space is euclidean. These conditions are related to the altitude of a triangle, they are the Altitude Property, the Isosceles Altitude Property, the Orthogonal Similarity Property or their Weak versions. The authors also show that a finitely compact, convex, externally convex metric space is congruent to a euclidean or hyperbolic space of finite dimension if it satisfies the Isosceles Intrinsic Altitude Property.