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

Explore with Wolfram|Alpha

Cite this as:

Weisstein, Eric W. "Line of Curvature." From MathWorld--A Wolfram Web Resource.

Subject classifications