View source for Indicatrix of tangents

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''of a curve $\Gamma$ in a Euclidean space $E^n$''

The curve $\Gamma^*$ on the sphere $S^{n-1}\subset E^n$ which assigns to the parameter value $\tau$ the point whose position vector is parallel to the tangent vectors at $\tau$ to $\Gamma$. In order that a spherical curve $L$ be the indicatrix of tangents of some closed curve in $E^n$ it is necessary and sufficient that $L$ is not confined to some open half-sphere (Krein's theorem).

====References====
<table><TR><TD valign="top">[1]</TD> <TD valign="top">  M.Ya. Vygodskii,   "Differential geometry" , Moscow-Leningrad  (1949)  (In Russian)</TD></TR></table>



====Comments====
The indicatrix of tangents is also called the spherical tangent image. See also [[Spherical indicatrix|Spherical indicatrix]].