Isometries of spheres

Everling, Ulrich

doi:10.1090/S0002-9939-1995-1277108-2

Isometries of spheres
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by Ulrich Everling PDF

Proc. Amer. Math. Soc. 123 (1995), 2855-2859 Request permission

Abstract:

In a Euclidean space of dimension two or more, any mapping that preserves unit distance is an isometry; this is the theorem of Beckmann and Quarles. We prove a similar theorem for spheres, assuming that a given distance less than a quarter great circle is preserved.

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