Eversion
A curve on the unit sphere 
is an eversion if it has no corners or cusps (but it may be self-intersecting). Theseproperties are guaranteed by requiring that the curve's velocity never vanishes. A mapping 
forms animmersion of the Circle into the Sphere Iff, for all 
,
Smale (1958) showed it is possible to turn a Sphere inside out (Sphere Eversion) using eversion.See also Sphere Eversion
References
Smale, S. ``A Classification of Immersions of the Two-Sphere.'' Trans. Amer. Math. Soc. 90, 281-290, 1958.
- Langlands Program
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- Laplace-Beltrami Operator
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