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Compute the first and second fundamental form

  1. Sep 22, 2014 #1


    xu = ( -r cos v sin u, -r sin v sin u, r cos u)

    xuu = ( -r cos v cos u, -r sin v cos u, -r sin u)

    xv = ( -(a + r cos u) sin v, (a + r cos u) cos v, 0)

    xvv = ( -(a + r cos u) cos v, - (a + r cos u) sin v, 0)

    xuv = ( r sin u sin v, -r sin u cos v, 0)

    E = [itex]x_u \cdot x_u [/itex]

    F = [itex]x_u \cdot x_v [/itex]

    G = [itex]x_v \cdot x_v [/itex]


    l = [itex]x_{uu} \cdot n [/itex]

    m = [itex]x_{uv} \cdot n [/itex]

    n = [itex]x_{vv} \cdot n [/itex]



    I'm not worried about the first fundamental forms. However, when I find the normal to use in computing the second fundamental forms, the equations are extremely cumbersome. Am I missing a simplification here or did I make an error in my derivation?
     
  2. jcsd
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