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Asymptotic curve
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== Properties == Asymptotic directions can only occur when the [[Gaussian curvature]] is negative (or zero). There are two asymptotic directions through every point with negative Gaussian curvature, bisected by the [[principal curvature|principal directions]]. There is one or infinitely many asymptotic directions through every point with zero Gaussian curvature. If the surface is [[Minimal surface|minimal]] and not flat, then the asymptotic directions are orthogonal to one another (and 45 degrees with the two principal directions). For a [[developable surface]], the asymptotic lines are the [[Generatrix|generatrices]], and them only. If a straight line is included in a surface, then it is an asymptotic curve of the surface.
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