  Riemannian cubics are critical points for the $L^2$ norm of acceleration of
curves in Riemannian manifolds $M$. In the present paper the $L^\infty$ norm
replaces the $L^2$ norm, and a less direct argument is used to derive necessary
conditions analogous to those for Riemannian cubics. The necessary conditions
are examined when $M$ is a sphere or a bi-invariant Lie group.
