Glasnik Matematicki, Vol. 39, No.2 (2004), 327-330.

UNIT-SPHERE PRESERVING MAPPINGS

Soon-Mo Jung and Byungbae Kim

Mathematics Section, College of Science and Technology, Hong-Ik University, 339-701 Chochiwon, Korea
e-mail: smjung@wow.hongik.ac.kr
e-mail: bkim@wow.hongik.ac.kr

Abstract.   We prove that if a one-to-one mapping f : Rn → Rn (n ≥ 2) preserves the unit n - 1 spheres (Sn -1), then f is a linear isometry up to translation.

2000 Mathematics Subject Classification.   51K05.

Key words and phrases.   Isometry, unit-circle preserving mapping.

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