On the Aleksandrov problem of conservative distances

Mielnik, Bogdan; Rassias, Themistocles M.

doi:10.1090/S0002-9939-1992-1101989-3

On the Aleksandrov problem of conservative distances
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by Bogdan Mielnik and Themistocles M. Rassias PDF

Proc. Amer. Math. Soc. 116 (1992), 1115-1118 Request permission

Abstract:

A case of the Aleksandrov problem for unit distance preserving mappings between metric spaces is solved. The relevance of methods used in mathematical foundations of quantum mechanics is shown for another case of Aleksandrov problem involving angular distances $\pi /2$ on the unit sphere.

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