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Is it possible to add a term like $\epsilon_{\alpha\beta\gamma\delta}R^{\alpha\beta}_{\enspace\mu\nu}R^{\mu\nu\gamma\delta}$ to the Gauss-Bonnet action in higher dimensional theories of gravity? Or can this term be expressed as a linear combination of $R^2$, $R_{\mu\nu}R^{\mu\nu}$ and $R_{\nu\mu\rho\sigma}R^{\nu\mu\rho\sigma}$? Thanks in advance!

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