Christoffel symbols knowing Line element (check my result)

Question

I'm asked to find all the non-zero Christoffel symbols given the following line element:

$ds^2=2x^2dx^2+y^4dy^2+2xy^2dxdy$

The result I have obtained is that the only non-zero component of the Christoffel symbols is:

$\Gamma^x_{xx}=\frac{1}{x}$

Is this correct?

Thanks!!!

Answer 1

It's incorrect, there are more non-zero symbols. Also, in my previous answer, I thought you meant to just check the one entry you specified. Here are all the symbols. I suggest looking into CAS's if you plan to compute many symbols.