On the Aleksandrov problem of conservative distances

Bogdan Mielnik, Themistocles M. Rassias
1992 Proceedings of the American Mathematical Society  
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 7t/2 on the unit sphere.
doi:10.1090/s0002-9939-1992-1101989-3 fatcat:kwoctlofrjdfzas5gcnlba2bse