First integrals from conformal symmetries: Darboux–Koenigs metrics and beyond
First integrals from conformal symmetries: Darboux–Koenigs metrics and beyond
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DOI：
10.1016/j.geomphys.2019.07.006
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发表时间：
2018-04
影响因子：
1.5
通讯作者：
A. Fordy
中科院分区：
文献类型：
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作者：
A. Fordy
在常曲率空间上，测地线方程自动具有高阶积分，这些高阶积分只是由一阶积分建立的，对应于Kill矢量的丰富性。这不再适用于一般的共形平坦空间，但在这种情况下，存在一个大型的共形对称代数。在本文中，我们利用这些共形对称来构造测地线方程的高阶积分。我们用这种方法给出了Darboux-Koenigs度规的一个新的推导，它只有一个Killing向量，但有两个二次积分。我们还考虑了具有一个杀伤向量和两个双积分的情况，该方法允许以更简单的方式构造量子模拟。
On spaces of constant curvature, the geodesic equations automatically have higher order integrals, which are just built out of first order integrals, corresponding to the abundance of Killing vectors. This is no longer true for general conformally flat spaces, but in this case there is a large algebra ofconformalsymmetries. In this paper we use these conformal symmetries to build higher order integrals for the geodesic equations. We use this approach to give a new derivation of the Darboux–Koenigs metrics, which have onlyoneKilling vector, but two quadratic integrals. We also consider the case of possessing one Killing vector and twocubicintegrals.The approach allows thequantumanalogue to be constructed in a simpler manner.