A line on a surface at each point of which the tangent has one of the principal directions. The curvature lines are defined by the equation
where $E,F,G$ are the coefficients of the first fundamental form of the surface, and $L,M,N$ those of the second fundamental form. The normals to the surface along curvature lines form a developable surface. The curvature lines on a surface of revolution are the meridians and the parallels of latitude. The curvature lines on a developable surface are its generators (which are straight lines) and the lines orthogonal to them.
|[a1]||D.J. Struik, "Differential geometry" , Addison-Wesley (1950)|
Curvature line. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Curvature_line&oldid=32954