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Line of Curvature


A curve on a surface whose tangents are always in the direction of principal curvature. The equation of the lines of curvature can be written

 |g_(11) g_(12) g_(22); b_(11) b_(12) b_(22); du^2 -dudv dv^2|=0,

where g and b are the coefficients of the first and second fundamental forms.


See also

Dupin's Theorem, Fundamental Forms, Principal Curvatures

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Cite this as:

Weisstein, Eric W. "Line of Curvature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LineofCurvature.html

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