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.

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.

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