Tangent Indicatrix
Let the Speed 
of a closed curve on the unit sphere 
never vanish. Then the tangent indicatrix
is another closed curve on
. It is sometimes called the Tantrix. If Immerses in , then so will 
.
References
Solomon, B. ``Tantrices of Spherical Curves.'' Amer. Math. Monthly 103, 30-39, 1996.