parabolic line

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In differential geometry, a smooth surface in three dimensions has a parabolic point when the Gaussian curvature is zero. Typically such points lie on a curve called the parabolic line

which separates the surface into regions of positive and negative Gaussian curvature.

Points on the parabolic line give rise to folds on the Gauss map: where a ridge crosses a parabolic line there is a cusp of the Gauss map.Ian R. Porteous (2001) Geometric Differentiation, Chapter 11 Ridges and Ribs, pp 182–97, Cambridge University Press {{isbn|0-521-00264-8}} .