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Indicatrix of tangents

From Encyclopedia of Mathematics
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of a curve in a Euclidean space

The curve on the sphere which assigns to the parameter value the point whose position vector is parallel to the tangent vectors at to . In order that a spherical curve be the indicatrix of tangents of some closed curve in it is necessary and sufficient that is not confined to some open half-sphere (Krein's theorem).

References

[1] M.Ya. Vygodskii, "Differential geometry" , Moscow-Leningrad (1949) (In Russian)


Comments

The indicatrix of tangents is also called the spherical tangent image. See also Spherical indicatrix.

How to Cite This Entry:
Indicatrix of tangents. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Indicatrix_of_tangents&oldid=32312
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article