Your R is actually the Ricci tensor, not the Riemann tensor. The Riemann tensor has four indices, not two. The Ricci tensor is formed by contracting the Riemann tensor on its first and third indices.
Your R is actually the Ricci tensor, not the Riemann tensor. The Riemann tensor has four indices, not two. The Ricci tensor is formed by contracting the Riemann tensor on its first and third indices.