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Normal-developable surface

This article defines a property that makes sense for a surface embedded in \R^3, viz three-dimensional Euclidean space. The property is invariant under orthogonal transformations and scaling, i.e., under all similarity transformations.
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Definition

A surface embedded in \R^3 is said to be normal-developable if there is a curve on the surface such that every normal to the curve also lies on the surface, and further, such that the unions of these normal lines is the whole surface.

Relation with other properties