A characterization of isometries on an open convex set,II |
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| Authors: | Soon-Mo Jung |
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| Institution: | (1) Mathematics Section College of Science and Technology, Hong-Ik University, 339-701 Chochiwon, Korea |
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| Abstract: | Let E
n
be an n-dimensional Euclidean space with n ≥ 2. In this paper, we generalize a classical theorem of Beckman and Quarles by proving that if a mapping, from an open convex
subset Co of E
n
into E
n
, preserves a distance ρ, then the restriction of f to an open convex subset C
∞ of C
0 is an isometry.
This work was supported by 2007 Hongik University Research Fund. |
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| Keywords: | Aleksandrov problem isometry distance preserving mapping restricted domain |
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