论文标题
在Step-Two和Step-Three Nilpotent Lie组上的第一个积分
First integrals on step-two and step-three nilpotent Lie groups
论文作者
论文摘要
本文的目的是研究对配备有剩余不变度度量的Nilpotent Lie群体的第一个积分流量的代数代数的代数关系。事实证明，$ k $ step nilpotent Lie Group的等轴测代数，$ k = 2,3 $，引起了地球流量的第一综合体系列。还分析了不变的第一积分，并显示了新的相关条件。最后，证明，在低维度中，可以通过杀死矢量场和对称杀死2汤匙场来构建完整的第一积分族。这适用于k-step nilpotent lie lie代数$ m \ leq 5 $和$ k = 2,3 $。还研究了第六维度的情况。
The goal of this paper is the study of algebraic relations on the Lie algebra of first integrals of the geodesic flow on nilpotent Lie groups equipped with a left-invariant metric. It is proved that the isometry algebra of the $k$-step nilpotent Lie group, $k=2,3$, gives rise to a isomorphic family of first integrals for the geodesic flow. Also invariant first integrals are analyzed and new involution conditions are shown. Finally it is proved that in low dimensions complete families of first integrals can be constructed with Killing vector fields and symmetric Killing 2-tensor fields. This holds for k-step nilpotent Lie algebras of dimension $m\leq 5$ and $k=2,3$. The situation in dimension six is also studied.
