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Edge of regression

From Encyclopedia of Mathematics
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A type of singularity of differentiable mappings (cf. Singularities of differentiable mappings) of a manifold into a Euclidean space. In the simplest case of a mapping of a surface into the three-dimensional Euclidean space an edge of regression represents a smooth curve in , with smooth image , such that for any the intersection of with the plane through and perpendicular to is a cusp. It occurs in the pseudo-sphere.


Comments

Cf. also the edge of regression of a developable surface.

An edge of regression is also called a cuspidal edge. It is the stable caustic of type , see [a1], p. 331.

References

[a1] V.I. Arnol'd, S.M. [S.M. Khusein-Zade] Gusein-Zade, A.N. Varchenko, "Singularities of differentiable maps" , 1 , Birkhäuser (1985) (Translated from Russian) MR777682 Zbl 0554.58001
How to Cite This Entry:
Edge of regression. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Edge_of_regression&oldid=31754
This article was adapted from an original article by M.I. Voitsekhovskii (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article