Author(s): Yoshihiko Tazawa
In this article we will show how to use Mathematica in dealing with curves
and surfaces in the three dimensional unit sphere S^ embedded in the four
dimensional Euclidian space E\ Since S* is the Lie group of unit quater-
nions and at the same time it is a space of constant curvature, the analogy
of the theory of curves in E^ holds.
We calculate curvature and torsion
of curves in S^ by Mathematica.
The Gauss map v of a surface in E^ is
decomposed into the two maps v+ and z/_.
If the surface is contained in 5^,
we can define another Gauss map z/g.
We use Mathematica to visualize the
shapes of the images of these Gauss maps.
Finally, the meaning of these
images becomes clear through the notion of the slant surface.
The space E* is re...
Size: 455 kb
Paper DOI: 10.2495/IMS970591
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