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## Minimum $L^\infty$ Accelerations in Riemannian Manifolds

### Abstract

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

Topics: Mathematics - Differential Geometry, Mathematics - Optimization and Control, 49K15 53C22 58E99 49Q99 Secondary: 70Q05
Year: 2011
OAI identifier: oai:arXiv.org:1104.2392