Differential geometry of surfaces | Surfaces

Parabolic line

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 linewhich 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. (Wikipedia).

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Related pages

Gaussian curvature | Gauss map | Differential geometry | Ridge (differential geometry)