## Isometries of spheres

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- by Ulrich Everling
- Proc. Amer. Math. Soc.
**123**(1995), 2855-2859 - DOI: https://doi.org/10.1090/S0002-9939-1995-1277108-2
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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.## References

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## Bibliographic Information

- © Copyright 1995 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**123**(1995), 2855-2859 - MSC: Primary 51F99; Secondary 51N20
- DOI: https://doi.org/10.1090/S0002-9939-1995-1277108-2
- MathSciNet review: 1277108