Transformation law for Christoffel symbol of first kind

[Will_C]

Hi,
I have met a problem, that is how to prove transformation law for Christoffel symbol of first kind. I have read books about that, but many of them just state: cyclic permutation of the 3 indices and substitution. When I tried to work out, I could not elimate some terms...
Can anyone show me how to prove it once.
Will.

 

[dextercioby]

Hi,
I have met a problem, that is how to prove transformation law for Christoffel symbol of first kind. I have read books about that, but many of them just state: cyclic permutation of the 3 indices and substitution. When I tried to work out, I could not elimate some terms...
Can anyone show me how to prove it once.
Will.

By prove,u mean calculate it,right??I'll give u the results and the calculations for the second kind symbols and let u strive to find the first kind symbols.

 

[Will_C]

Thx dextercioby,
I think ,what I have read, is a old style Tensor. So most books, I have read, derive the second kind transformation law from the first kind. Thank you very much for your help. It would be more happy to me if I can get some derives base on the style, what I am learning.

Will.

 

[dextercioby]

Thx dextercioby,
I think ,what I have read, is a old style Tensor. So most books, I have read, derive the second kind transformation law from the first kind. Thank you very much for your help. It would be more happy to me if I can get some derives base on the style, what I am learning.

Will.

No,what u've read was a about 90% of a page from a pdf-format book on GR.That's why it used Greek suffixes.If it's old style,well,i doubt it,since he takes diff.geometry from zero,from the definition of a topological space.
I believe u can manipulate suffices,derivatives and other tensorial quantities so that u can get the first kind symbols' transformation law directly from the expression of a covariant derivative of a covector.

Daniel.

 

[hyjta]

thanks .