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Christoffel Symbols

  • Thread starter Lee33
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Homework Statement



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

Homework 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}##

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)##?

I just need help getting started. Thanks for your time!
 

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