Curvature line

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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 are the coefficients of the first fundamental form of the surface, and 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)
How to Cite This Entry:
Curvature line. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.B. Ivanov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article