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Transformation law for Christoffel symbol of first kind

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Will_C
#1
Dec6-04, 04:15 AM
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.
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dextercioby
#2
Dec6-04, 01:38 PM
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Quote 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
File Type: doc Christoffel symbols of the second kind.doc (48.5 KB, 328 views)
Will_C
#3
Dec7-04, 04:11 AM
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.

dextercioby
#4
Dec7-04, 06:48 AM
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Transformation law for Christoffel symbol of first kind

Quote 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.
hyjta
#5
May24-09, 03:54 AM
P: 1
thanks .


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