  Riemannian cubics in tension are critical points of the linear combination of
two objective functionals, namely the squared norms of the velocity and
acceleration of a curve on a Riemannian manifold. We view this variational
problem of finding a curve as a multi-objective optimization problem and
construct the Pareto fronts for some given instances where the manifold is a
sphere and where the manifold is a torus. The Pareto front for the curves on
the torus turns out to be particularly interesting: the front is disconnected
and it reveals two distinct Riemannian cubics with the same boundary data,
which is the first known nontrivial instance of this kind. We also discuss some
convexity conditions involving the Pareto fronts for curves on general
Riemannian manifolds.
