Show that the parallel (cycles) of a surface of revolution are curvature lines!

Thank you very much in advance!

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- Dec 13th 2011, 05:01 AMzadirParallel of surface of revolution
Show that the parallel (cycles) of a surface of revolution are curvature lines!

Thank you very much in advance! - Dec 13th 2011, 06:30 AMxxp9Re: Parallel of surface of revolution
By symmetry the direction of the generatrix is a critical point of the function of normal curvature, at a fixed point, so it is one of the principle directions.

So the other principle direction is the one orthogonal to it, that is, the direction of the parallel cycles.