On characterizations of sphere-preserving maps

• Autores: Baokui Li, Guowu Yao
• Localización: Mathematical proceedings of the Cambridge Philosophical Society, ISSN 0305-0041, Vol. 147, Nº 2, 2009, págs. 439-446
• Idioma: inglés
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• Resumen

  • Recently, the first author and Y. Wang proved that (n = 2) is a Möbius transformation if and only if f is a non-degenerate circle-preserving map. In this paper, we will further the result to show that f is a Möbius transformation if and only if f is a non-degenerate r�dimensional sphere-preserving map. The versions for the Euclidean and hyperbolic cases are also obtained. These results make no surjectivity or injectivity or even continuity assumptions on f. Moreover, certain degenerate sphere-preserving maps are given, which completes the characterizations of sphere-preserving maps.