Summary: We tackle the problem of the estimation of the level sets \(L_f ( \lambda )\) of the density \(f\) of a random vector \(X\) supported on a smooth manifold \(M \subset \mathbb{R}^d\), from an iid sample of \(X\). To do that we introduce a kernel-based estimator \(\hat{f}_{n,h} \), which is a slightly modified version of the one proposed in Rodríguez-Casal and Saavedra-Nieves (2014) and proves its a.s. uniform convergence to \(f\). Then, we propose two estimators of \(L_f ( \lambda )\), the first one is a plug-in: \( L_{\hat{f}_{n,h}} ( \lambda )\), which is proven to be a.s. consistent in Hausdorff distance and distance in measure, if \(L_f ( \lambda )\) does not meet the boundary of \(M\). While the second one assumes that \(L_f ( \lambda )\) is \(r\)-convex, and is estimated by means of the \(r\)-convex hull of \(L_{\hat{f}_{n,h}} ( \lambda )\). 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.