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[tex] \left( \nabla_\mu \nabla_\beta - \nabla_\beta \nabla_\mu \right) V^\mu = R_{\nu \beta} V^\nu [/tex]

Can since all the terms involving ##\mu## on the left and ##\nu## on the right are contractions, can I simply do:

[tex]\left( \nabla^\mu \nabla_\beta - \nabla_\beta \nabla^\mu \right) V_{\mu} = R^\nu_{\beta} V_{\nu} [/tex]?

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# Can I simply reverse the indices in a contraction?

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