ar X iv : m at h / 03 07 21 6 v 1 [ m at h . D G ] 1 6 Ju l 2 00 3 COISOTROPIC VARIATIONAL PROBLEMS

نویسنده

  • JAMES D. E. GRANT
چکیده

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 pro-jective, conformal and pseudo-conformal arc-length functionals, the Delaunay and the Poincaré variational problems.

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تاریخ انتشار 2003