Coisotropic Variational Problems
Differential Geometry
2007-05-23 v1
Abstract
In this article we study constrained variational problems in one independent variable defined on the space of integral curves of a Frenet system in a homogeneous space G/H. We prove that if the Lagrangian is G-invariant and coisotropic then the extremal curves can be found by quadratures. Our proof is constructive and relies on the reduction theory for coisotropic optimal control problems. This gives a unified explanation of the integrability of several classical variational problems such as the total squared curvature functional, the projective, conformal and pseudo-conformal arc-length functionals, the Delaunay and the Poincar{\'e} variational problems.
Cite
@article{arxiv.math/0307216,
title = {Coisotropic Variational Problems},
author = {James D. E. Grant and Emilio Musso},
journal= {arXiv preprint arXiv:math/0307216},
year = {2007}
}