  Curvilinear nanomagnets can support magnetic skyrmions stabilized at a local
curvature without any intrinsic chiral interactions. Here, we propose a new
mechanism to stabilize chiral N\'{e}el skyrmion states relying on the
\textit{gradient} of curvature. We illustrate our approach with an example of a
magnetic thin film with perpendicular magnetic anisotropy shaped as a circular
indentation. We show that in addition to the topologically trivial ground
state, there are two skyrmion states with winding numbers $\pm 1$ and a
skyrmionium state with a winding number $0$. These chiral states are formed due
to the pinning of a chiral magnetic domain wall at a bend of the
nanoindentation due to spatial inhomogeneity of the curvature-induced
Dzyaloshinskii--Moriya interaction. The latter emerges due to the gradient of
the local curvature at a bend. While the chirality of the skyrmion is
determined by the sign of the local curvature, its radius can be varied in a
broad range by engineering the position of the bend with respect to the center
of the nanoindentation. We propose a general method, which enables one to
reduce a magnetic problem for any surface of revolution to the common planar
problem by means of proper modification of constants of anisotropy and
Dzyaloshinskii--Moriya interaction.
