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1990 (Publication #57)

Geometry of the Hopf Mapping and Pinkall's Tori of Given Conformal Type Computers in Geometry

Marcel Dekker, New York (1990) 57-62.

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ABSTRACT

The Hopf mapping from the 3-sphere to the 2-sphere and its investigation using computer graphics were discussed at the Conference on Computers in Geometry and Topology. Ulrich Pinkall gave a presentation in which he determined the conformal structure of tori obtained by lifting a closed curve on the 2-sphere under the Hopf mapping. This paper is a discussion of Pinkall's results, and it is an excellent example of a problem for which computergraphics are useful.