  The aim of this note is to answer several open problems arising from the
geometric description of the $m$-cluster categories of type $A_n$ and their
realization in terms of the $m$-th power of a translation quiver. In
particular, we give a geometric interpretation of the triangulated structure of
$m$-cluster categories. Furthermore, we characterize all the connected
components arising from a cluster category when taking the $m$-th power of its
Auslander-Reiten quiver.
