This paper is related to the issue of the density estimation of observations with values in a Riemannian submanifold. In this setting, Pelletier (2005) has proposed a kernel density estimator for independent data. We investigate here the behavior of Pelletier's estimator when the observations are generated from a strictly stationary α−mixing process, with values in this submanifold. In particular, we study the pointwise as well as the uniform weak and strong consistency of the estimator. Namely, we give the rate of convergence in mean square error meaning, in probability and almost surely. We also give a central-limit theorem and illustrate our purpose through some simulations and a real data application.