Geodesics as products of one-parameter subgroups in compact lie groups and homogeneous spaces
Geodesics as products of one-parameter subgroups in compact lie groups and homogeneous spaces
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作为紧李群和齐次空间中单参数子群的乘积的测地线
DOI：
10.1002/mana.202000282
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发表时间：
2023
影响因子：
1
通讯作者：
Souris N
中科院分区：
文献类型：
--
作者：
Souris N
研究了紧李群G和齐性空间G/H$G/H$的测地线方程，证明了测地线是G的单参数子群的乘积exp（tX 1）<$exp（tXN）$\exp（tX_1）\cdots \exp（tX_N）$的轨道，只要满足黎曼度量的一个简单代数条件.对于SO（3）SO（3），我们把这类测地线与对称顶的自由运动联系起来。此外，通过使用一系列的李群G，我们构造了大量的度量具有上述类型的测地线。
We study the geodesic equation for compact Lie groupsGand homogeneous spaces G/H$G/H$, and we prove that the geodesics are orbits of products exp(tX1)⋯exp(tXN)$\exp (tX_1)\cdots \exp (tX_N)$ of one‐parameter subgroups ofG, provided that a simple algebraic condition for the Riemannian metric is satisfied. For the group SO(3)$SO(3)$, we relate this type of geodesics to the free motion of a symmetric top. Moreover, by using series of Lie subgroups ofG, we construct a wealth of metrics having the aforementioned type of geodesics.