Abstract : Concerning the integrability of almost K\"ahler manifolds, we prove that a compact almost K\"ahler locally symmetric space is K\"ahler if the length of the star Ricci tensor is not smaller than that of the Ricci tensor.
Keywords : integrability of almost K\"ahler manifoldsmanifolds, compact almost K\"ahler locally symmetric space, K\"ahler, the length of the star Ricci tensor, the length of the Ricci tensor
