On first integrals of the geodesic flow on Heisenberg nilmanifolds
On first integrals of the geodesic flow on Heisenberg nilmanifolds
复制标题
海森堡尼尔流形上测地线流的一阶积分
DOI：
10.1016/j.difgeo.2016.08.004
复制
发表时间：
2016
影响因子：
0.5
通讯作者：
Silvio Reggiani
中科院分区：
文献类型：
--
作者：
Alejandro Kocsard;G. Ovando;Silvio Reggiani
本文研究了具有左不变度量的诣零流形上的测地线流。我们写的基本定义，并找到一般公式的泊松对合。作为应用，我们发展了海森堡李群配备了它的正则度量。我们证明了一族给出完全可积性的首次积分可以在等距群的李代数上读出。我们还解释了对任何不变度量和紧度量的完全可积性。
In this paper we study the geodesic flow on nilmanifolds equipped with a left-invariant metric. We write the underlying definitions and find general formulas for the Poisson involution. As an application we develop the Heisenberg Lie group equipped with its canonical metric. We prove that a family of first integrals giving the complete integrability can be read off at the Lie algebra of the isometry group. We also explain the complete integrability for any invariant metric and on compact quotients.