Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems
Periodic orbits in magnetic fields and Ricci curvature of Lagrangian systems
复制标题
磁场中的周期轨道和拉格朗日系统的里奇曲率
DOI：
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发表时间：
1995
期刊：
影响因子：
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通讯作者：
I. Taimanov
中科院分区：
文献类型：
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作者：
Abbas Bahri;I. Taimanov
其中dA-F，在流形Mn上的闭曲线空间上。这里A是1-形式（即，F是一个精确的2-形式）。该泛函是通常的长度泛函的自然推广，并且当动能由度量张量定义并且形式F定义磁场时，其闭极值对应于黎曼流形Mn上的粒子运动的周期性轨迹。这个泛函也对应于经典力学和数学物理的其他问题的周期轨道，如[N2]，[N3]，[NS]中所示。当拉格朗日函数
where dA -F, on the space of closed curves on the manifold Mn. Here A is a 1-form (i.e., F is an exact 2-form). This functional is a natural generalization of the usual functional of length, and its closed extremals correspond to periodic trajectories of the motion of particles on the Riemannian manifold Mn when the kinetic energy is defined by the metric tensor and the form F defines a magnetic field. Also this functional corresponds to the periodic orbits for other problems of classical mechanics and mathematical physics, as it was shown in [N2], [N3], [NS]. When the Lagrangian function