论文标题
海森堡流形的周期性磁性测量学
Periodic Magnetic Geodesics on Heisenberg Manifolds
论文作者
论文摘要
我们研究海森堡组上磁流的动力学。令$ h $表示三维连接的海森堡谎言组，并具有左右不变的里曼尼亚式公制和精确的左右磁场。令$γ$为$ h，$的晶格子组，以便$γ\ Backslash H $是封闭的Nilmanifold。我们首先在$ h $上找到对磁性测量学的明确描述，然后确定所有封闭的磁性大地测量学及其长度的$γ\ Backslash H $。然后，我们考虑这些结果的两个应用：周期性磁性测量学的密度和明显的磁长度刚度。
We study the dynamics of magnetic flows on Heisenberg groups. Let $H$ denote the three-dimensional simply connected Heisenberg Lie group endowed with a left-invariant Riemannian metric and an exact, left-invariant magnetic field. Let $Γ$ be a lattice subgroup of $H,$ so that $Γ\backslash H$ is a closed nilmanifold. We first find an explicit description of magnetic geodesics on $H$, then determine all closed magnetic geodesics and their lengths for $Γ\backslash H$. We then consider two applications of these results: the density of periodic magnetic geodesics and marked magnetic length spectrum rigidity.
