I'm using xAct package to compute the curvature tensor from a specific connection, of the form $\Gamma^a_{bc}=\left\{^{\:a}_{bc}\right\} + S^a_{\;bc}$, where the first term is the Levi Civita connection constructed from the metric of the manifold, and the second term is the shift tensor which depends on a vector field $f_k$ : $S^a_{\;bc}=(\delta^a_bf_c+\delta^a_cf_b-g_{bc}f^a)$. I would like to find the curvature tensor, Ricci tensor, and eventually the Ricci scalar related to this connection. However, i'm having a hard time trying to apply Simplification to the curvature tensor, and RicciScalar[] does not give me the desired result.

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