Principal curvature

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In differential geometry, the two principal curvatures at a given point of a differentiable surface in Euclidean space are the minimum and maximum of the curvatures at that point of all the curves on the surface passing through the point. Here the curvature of a curve is taken to be the reciprocal of the radius of the osculating circle. The directions of minimum and maximum curvature are always perpendicular (or arbitrary, in the case when the two values are equal). For a developable surface, at least one of the principal curvatures is zero at every point. For a minimal surface, the two principal curvatures are equal and opposite at every point.

See also: Mean curvature, curvature