ar X iv : m at h - ph / 0 30 70 15 v 1 8 J ul 2 00 3 Integrable geodesic flows on Riemannian manifolds : Construction and Obstructions ∗ Alexey
نویسنده
چکیده
This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.
منابع مشابه
ar X iv : m at h - ph / 0 30 70 16 v 1 8 J ul 2 00 3 Nonholonomic LR systems as Generalized Chaplygin systems with an Invariant Measure and Geodesic Flows on Homogeneous Spaces ∗
We consider a class of dynamical systems on a Lie group G with a leftinvariant metric and right-invariant nonholonomic constraints (so called LR systems) and show that, under a generic condition on the constraints, such systems can be regarded as generalized Chaplygin systems on the principle bundle G → Q = G/H , H being a Lie subgroup. In contrast to generic Chaplygin systems, the reductions o...
متن کاملar X iv : m at h - ph / 0 40 80 37 v 1 2 4 A ug 2 00 4 Integrable nonholonomic geodesic flows on compact Lie groups ∗
This paper is a review of recent results on integrable nonholonomic geodesic flows of left–invariant metrics and leftand right–invariant constraint distributions on compact Lie groups.
متن کاملar X iv : m at h - ph / 0 60 20 16 v 2 3 A pr 2 00 6 Magnetic Geodesic Flows on Coadjoint Orbits ∗ † ‡
We describe a class of completely integrable G-invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group G with magnetic field given by the Kirillov-Konstant 2-form.
متن کاملar X iv : m at h - ph / 0 60 20 16 v 1 7 F eb 2 00 6 Magnetic Geodesic Flows on Coadjoint Orbits ∗
We describe a class of completely integrable G-invariant magnetic geodesic flows on (co)adjoint orbits of a compact connected Lie group G with magnetic field given by the Kirillov-Konstant 2-form.
متن کاملar X iv : m at h - ph / 0 31 00 10 v 1 8 O ct 2 00 3 Obstructions , Extensions and Reductions . Some applications of Cohomology ∗
After introducing some cohomology classes as obstructions to orientation and spin structures etc., we explain some applications of cohomology to physical problems, in especial to reduced holonomy in M and F -theories.
متن کامل