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Math Help - Given first fundamental form, find gaussian curvature

  1. #1
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    Given first fundamental form, find gaussian curvature

    Show that if the first fundamental form with respect to the given parametrization x(u,v) of a surface has the form
    du2+2cosw(u,v)dudv+dv2 for some function w, then the gaussian curvature K=-wuv/sinw.

    Attempt:
    E=1
    F=cosw(u,v)
    G=1

    K=eg-f2/EG-F2

    I don't know how to find the 2nd fundamental form coefficients with the given information. Or is there another way to solve?
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  2. #2
    Super Member Rebesques's Avatar
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    Re: Given first fundamental form, find gaussian curvature

    Remember that the curvature depends only on the coefficients of the first fundamental form. There exists a very tedious formula for this.
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