- #1

zn5252

- 72

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hello ,

In the Bianchi Identities of the second kind, we have ∇a R

but since ∇c R

we get :

∇a R

in the last term, we exchange the c and the b indices and we would arrive at:

∇a R

which leads to :

∇a R

but this incorrect ? did I do something wrong ?

I would like actually to arrive at the formula :

2 ∇b R

see formula 9 here from original Bel's article from 1938:

http://gallica.bnf.fr/ark:/12148/bp...ction+d'un+tenseur+du+quatrième+ordre;.langEN

and

(see formula 5 here : https://docs.google.com/viewer?a=v&...9JJLhB&sig=AHIEtbRUONCiZUSV_8erdxK9YSMiouUrjA)

Thanks,

cheers,

In the Bianchi Identities of the second kind, we have ∇a R

_{bcde}+ ∇b R_{cade}+ ∇c R_{abde}≡ 0but since ∇c R

_{abde}= - ∇c R_{bade}we get :

∇a R

_{bcde}+ ∇b R_{cade}- ∇c R_{bade}= 0in the last term, we exchange the c and the b indices and we would arrive at:

∇a R

_{bcde}+ ∇b R_{cade}- ∇b R_{cade}= 0which leads to :

∇a R

_{bcde}= 0 .but this incorrect ? did I do something wrong ?

I would like actually to arrive at the formula :

2 ∇b R

_{acde}− ∇a R_{bcde}≡ 0.see formula 9 here from original Bel's article from 1938:

http://gallica.bnf.fr/ark:/12148/bp...ction+d'un+tenseur+du+quatrième+ordre;.langEN

and

(see formula 5 here : https://docs.google.com/viewer?a=v&...9JJLhB&sig=AHIEtbRUONCiZUSV_8erdxK9YSMiouUrjA)

Thanks,

cheers,

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