Minimum $L^infty$ Accelerations in Riemannian Manifolds

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.