  We prove quartic convergence of cubic spline interpolation for curves into
Riemannian manifolds as the grid size of the interpolation grid tends to zero.
In contrast to cubic spline interpolation in Euclidean space, where this result
is classical, the interpolation operator is no longer linear. Still, concepts
from the linear setting may be generalized to the Riemannian case, where we try
to use intrinsic Riemannian formulations and avoid charts as much as possible.
