Transformation law for Christoffel symbol of first kind

by Will_C
Tags: christoffel, kind, symbol, transformation
 P: n/a 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.
HW Helper
P: 11,717
 Quote by 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.
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.
Attached Files
 Christoffel symbols of the second kind.doc (48.5 KB, 326 views)
 P: n/a 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.
HW Helper
P: 11,717

Transformation law for Christoffel symbol of first kind

 Quote by 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.
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 definiton of a topological space.
I beleive 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.
 P: 1 thanks .

 Related Discussions Special & General Relativity 7 Math & Science Software 2 Special & General Relativity 9 Special & General Relativity 10 Differential Geometry 20