We tackle the problem of the estimation of the level sets L f (λ) of the density f of a random vector X supported on a smooth manifold M⊂ R d, from an iid sample of X. To do that we introduce a kernel-based estimator f ˆ n, h, which is a slightly modified version of the one proposed in Rodríguez-Casal and Saavedra-Nieves (2014) and proves its as uniform convergence to f. Then, we propose two estimators of L f (λ), the first one is a plug-in: L f ˆ n, h (λ), which is proven to be as consistent in Hausdorff distance and distance in measure, if L f (λ) does not meet the boundary of M. While the second one assumes that L f (λ) is r-convex, and is estimated by means of the r-convex hull of L f ˆ n, h (λ). The performance of our proposal is illustrated through some simulated examples. In a real data example we analyze the intensity and direction of strong and moderate winds.