Computing the second fundamental form - can you spot the error?

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Homework Statement

Compute the second fundamental form of the surface.

Relevant Equations

Standard differential geometry formulas for the second fundamental form with Christoffel symbols.

Hi all. We are computing the second fundamental form corresponding to a surface.

The correct answer should give the coefficients 2, 0, and -2 for II_uu, II_uv, II_vv

We have only been able to compute II^z, and not II^x, II^y where we have functions instead of 2, 0 and -2.

We are 99% certain that everything up to the da component in part (e.) is correct. It is just in the last computations where an apparent errors are. Can you see where the error is in part g?

In part g, the II's corresponding to x and y should be the same as z. It seems like something is missing, perhaps. The second fundamental form were calculated using the following formula.

Thank you!

 

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