Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Isometries of spheres

Author: Ulrich Everling
Journal: Proc. Amer. Math. Soc. 123 (1995), 2855-2859
MSC: Primary 51F99; Secondary 51N20
MathSciNet review: 1277108
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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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Keywords: Isometry, sphere, projective plane, Beckmann-Quarles theorem
Article copyright: © Copyright 1995 American Mathematical Society