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

Thank you very much in advance!

Printable View

- December 13th 2011, 04:01 AMzadirParallel of surface of revolution
Show that the parallel (cycles) of a surface of revolution are curvature lines!

Thank you very much in advance! - December 13th 2011, 05:30 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.