I am confused about the contraction in the proof of the contracted Bianchi identities in(adsbygoogle = window.adsbygoogle || []).push({});

https://en.wikipedia.org/wiki/Proofs_involving_covariant_derivatives

from the step

[tex] {g^{bn}}(R_{bmn;l}^m - R_{bml;n}^m + R_{bnl;m}^m) = 0[/tex]

it seems that the following two quantities are equal

[tex]{g^{bn}}R_{bml;n}^m = R_{l;n}^n[/tex]

[tex]- {g^{bn}}R_{bnl;m}^m = R_{l;m}^m[/tex]

but I don't understand how is this done if I write them explicitly

[tex]{g^{bn}}({\nabla _n}R)_{bml}^m[/tex]

[tex]- {g^{bn}}({\nabla _m}R)_{bnl}^m[/tex]

Can anybody help me? I am new to this field and I feel there is something missing. Please help to point out.

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# A Difficulty in understanding contracted Bianchi identities

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