Minimum $L^\infty$ Accelerations in Riemannian Manifolds

Lyle Noakes

Minimum $L^\infty$ Accelerations in Riemannian Manifolds

Differential Geometry 2011-04-14 v1 Optimization and Control

Authors: Lyle Noakes

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.

Keywords

riemannian geometry

Cite

@article{arxiv.1104.2392,
  title  = {Minimum $L^\infty$ Accelerations in Riemannian Manifolds},
  author = {Lyle Noakes},
  journal= {arXiv preprint arXiv:1104.2392},
  year   = {2011}
}

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