Suppose we consider a Riemannian manifold and a local orthonormal frame $\{Y_i\}$. I was wondering whether, for the Riemann curvature tensor $R$, there are identities with regards to expressions of the form $$ \langle R(Y_i,Y_j)Y_k, Y_l \rangle $$ over and above the standard identities that one can find on Wikipedia. (The particular property that one has is the orthonormality of the vector fields $Y_i,Y_j,Y_k,Y_l$.)
Many thanks!