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Christoffel Symbols

  1. Dec 2, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the Christoffel symbols of a surface in the form ##g= f(u,v).##

    2. Relevant equations

    ##f_{u_1u_1} = \Gamma^1_{11} f_{u_1} + \Gamma^2_{11}f_{u_2} + A \vec{N}##
    ##f_{u_1u_2} = f_{u_2u_1} = \Gamma^1_{12} f_{u_1} + \Gamma^2_{12}f_{u_2} + B \vec{N}##
    ##f_{u_2u_2} = \Gamma^1_{22} f_{u_1} + \Gamma^2_{22}f_{u_2} + C\vec{N}##


    3. The attempt at a solution

    I know how to calculate the Christoffel symbols if it explicitly shows a parameterized surface but how can I calculate it of the form ##g= f(u,v)?##
     
  2. jcsd
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