  We investigate density estimation from a $n$-sample in the Euclidean space
$\mathbb R^D$, when the data is supported by an unknown submanifold $M$ of
possibly unknown dimension $d < D$ under a reach condition. We study
nonparametric kernel methods for pointwise loss, with data-driven bandwidths
that incorporate some learning of the geometry via a local dimension estimator.
When $f$ has H\"older smoothness $\beta$ and $M$ has regularity $\alpha$, our
estimator achieves the rate $n^{-\alpha \wedge \beta/(2\alpha \wedge \beta+d)}$
and does not depend on the ambient dimension $D$ and is asymptotically minimax
for $\alpha \geq \beta$. Following Lepski's principle, a bandwidth selection
rule is shown to achieve smoothness adaptation. We also investigate the case
$\alpha \leq \beta$: by estimating in some sense the underlying geometry of
$M$, we establish in dimension $d=1$ that the minimax rate is
$n^{-\beta/(2\beta+1)}$ proving in particular that it does not depend on the
regularity of $M$. Finally, a numerical implementation is conducted on some
case studies in order to confirm the practical feasibility of our estimators.
