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
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.
منابع مشابه
ar X iv : m at h / 03 09 40 8 v 2 [ m at h . D G ] 1 2 Ju l 2 00 4 EINSTEIN METRICS ON SPHERES
متن کامل
ar X iv : m at h / 03 07 23 0 v 1 [ m at h . A G ] 1 6 Ju l 2 00 3 EXPLICIT EQUATIONS OF SOME ELLIPTIC MODULAR SURFACES
We present explicit equations of semi-stable elliptic surfaces (i.e., having only type In singular fibers) which are associated to the torsion-free genus zero congruence subgroups of the modular group as classified by A. Sebbar.
متن کاملar X iv : m at h / 02 07 29 6 v 1 [ m at h . M G ] 3 1 Ju l 2 00 2 Products of hyperbolic metric spaces
Let (Xi, di), i = 1, 2, be proper geodesic hyperbolic metric spaces. We give a general construction for a " hyperbolic product " X1× h X2 which is itself a proper geodesic hyperbolic metric space and examine its boundary at infinity.
متن کاملar X iv : 0 80 7 . 00 58 v 2 [ m at h . D G ] 1 6 Ju l 2 00 8 EQUIVARIANT DIFFERENTIAL CHARACTERS AND SYMPLECTIC REDUCTION
We describe equivariant differential characters (classifying equi-variant circle bundles with connections), their prequantization, and reduction.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003