论文标题
低维谎言代数中的大地载体的稳定性
Stability of geodesic vectors in low-dimensional Lie algebras
论文作者
论文摘要
如果其切线向量向左倾斜到身份，则具有左不变度度量的谎言组中的自然参数化曲线是一种地理位置。 Euler方程的固定点（平衡）称为地球矢量：从地球矢量方向始于身份的大地测量向量是$ g $的单参数亚组。我们将Lyapunov稳定和不稳定的地质矢量进行完整分类，用于尺寸$ 3 $的度量代数，以及尺寸的单模型公制谎言代数$ 4 $。
A naturally parameterised curve in a Lie group with a left invariant metric is a geodesic, if its tangent vector left-translated to the identity satisfies the Euler equation $\dot{Y}=\operatorname{ad}^t_YY$ on the Lie algebra $\mathfrak{g}$ of $G$. Stationary points (equilibria) of the Euler equation are called geodesic vectors: the geodesic starting at the identity in the direction of a geodesic vector is a one-parameter subgroup of $G$. We give a complete classification of Lyapunov stable and unstable geodesic vectors for metric Lie algebras of dimension $3$ and for unimodular metric Lie algebras of dimension $4$.
