Abstract
Historically, the stereographic projection and the Mercator projection must have appeared to mathematicians very startling. It was an indication that the conformai maps among the surfaces have far more flexibility than for example the isometries among surfaces, or line-preserving maps among planar domains. This was confirmed by Gauss in his A general solution to the problem of mapping parts of a given surface onto another surface such that the image and the mapped parts are similar in the smallest parts. This is esentially the existence of “isothermal co-ordinates” in the C ω case. It is interesting to note that this study preceded and partially motivated Gauss’s later foundational work on the notion of curvature. For an account of this interesting history see Dombrowski [D], pp 127–130.
Partially supported by the Max-Planck-Institut für Mathematik, Bonn, and an NSF grant.
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© 1988 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH, Braunschweig
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Kulkarni, R.S. (1988). Conformal Structures and Möbius Structures. In: Kulkarni, R.S., Pinkall, U. (eds) Conformal Geometry. Aspects of Mathematics / Aspekte der Mathematik, vol 12. Vieweg+Teubner Verlag, Wiesbaden. https://doi.org/10.1007/978-3-322-90616-8_1
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