# Please prove this

1. Jan 6, 2008

### Arham

Hello. I'm learning tensor analysis. I have a problem. We know that

$$\Gamma^i_{jk}=\vec{\epsilon^i}\cdot\frac{\partial\vec{\epsilon_j}}{\partial q^k}$$

Please prove the relation

$$\frac{\partial\vec{\epsilon_j}}{\partial q^k}=\Gamma^m_{jk}\vec{\epsilon_m}$$

Thanks very much in advance

Last edited: Jan 6, 2008
2. Jan 6, 2008

### belliott4488

What'll you pay me?

3. Jan 21, 2008

### hanskuo

$$\Gamma^m_{jk}\vec{\epsilon_m}\cdot\vec{\epsilon^i} =\Gamma^m_{jk}\delta^i{}_m=\Gamma^i_{jk}$$

4. Jan 23, 2008

### Arham

Thanks hanskuo.

I knew this proof, but I thought that it is only correct for the inverse relation. I was wrong!

5. Jan 24, 2008

### hanskuo

you are wellcome, Arham

Now I'm learning Differential Geometry,too.
do you begin to lerane covariant derivatives or not ?

6. Jan 24, 2008

### Arham

I'm an undergraduate physics student, hanskuo. I am learning tensor analysis from George Arfken's book. As you know, this book has a brief introduction to Covariant Derivative; I have read it. But I should do more exercises and read more about it in future.

7. Jan 24, 2008

### hanskuo

There are a lot of things interesting for covariant derivatives.
your original question likes this:
$$\nabla_{e_i}e_j=\Gamma^k{}_{ij}e_k$$

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