  We show how the newly developed method of Periodic Unfolding on Riemannian
manifolds can be applied to PDE problems: We consider the homogenization of an
elliptic model problem. In the limit, we obtain a generalization of the
well-known limit- and cell-problem. By constructing an equivalence relation of
atlases, one can show the invariance of the limit problem with respect to this
equivalence relation. This implies e.g. that the homogenization limit is
independent of change of coordinates or scalings of the reference cell.
