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
 |
where 
and 
are the coefficients of the first and second fundamental
forms.
Line of Curvature
See also
Dupin's Theorem, Fundamental Forms, Principal CurvaturesExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Line of Curvature." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LineofCurvature.html