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Math Help - Parallel of surface of revolution

  1. #1
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    Parallel of surface of revolution

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

    Thank you very much in advance!
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  2. #2
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    Re: 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.
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