The fact that image data samples lie on a manifold has been successfully exploited in many learning and inference problems. In this paper we leverage the specific structure of data in order to improve recognition accuracies in general recognition tasks. In particular we propose a novel framework that allows to embed manifold priors into sparse representation-based classification (SRC) approaches. We also show that manifold constraints can be transferred from the data to the optimized variables if these are linearly correlated. Using this new insight, we define an efficient alternating direction method of multipliers (ADMM) that can consistently integrate the manifold constraints during the optimization process. This is based on the property that we can recast the problem as the projection over the manifold via a linear embedding method based on the Geodesic distance. The proposed approach is successfully applied on face, digit, action and objects recognition showing a consistently increase on performance when compared to the state of the art.