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Altitude properties and characterizations of inner product spaces. (English) Zbl 0966.51009

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.

MSC:

51K05 General theory of distance geometry
46C15 Characterizations of Hilbert spaces
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References:

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