Lie and Noether symmetries of geodesic equations and collineations
Lie and Noether symmetries of geodesic equations and collineations
复制标题
测地方程和共线的李对称性和诺特对称性
DOI：
10.1007/s10714-010-1054-9
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发表时间：
2010
影响因子：
2.8
通讯作者：
A. Paliathanasis
中科院分区：
文献类型：
--
作者：
M. Tsamparlis;A. Paliathanasis
利用度量的特殊射影群及其退化群（仿射向量、位似向量和Killing向量）计算了黎曼空间中测地线方程的Lie对称性。用度量的位似向量和Killing向量给出了相同方程的Noether对称性。证明了黎曼空间中的测地线方程允许三个线性首次积分和两个二次首次积分。我们将结果应用于爱因斯坦空间、史瓦西时空和弗里德曼罗伯逊步行者时空的情形。在每种情况下，李和诺特对称性的计算明确连同相应的线性和二次第一积分。
The Lie symmetries of the geodesic equations in a Riemannian space are computed in terms of the special projective group and its degenerates (affine vectors, homothetic vector and Killing vectors) of the metric. The Noether symmetries of the same equations are given in terms of the homothetic and the Killing vectors of the metric. It is shown that the geodesic equations in a Riemannian space admit three linear first integrals and two quadratic first integrals. We apply the results in the case of Einstein spaces, the Schwarzschild spacetime and the Friedman Robertson Walker spacetime. In each case the Lie and the Noether symmetries are computed explicitly together with the corresponding linear and quadratic first integrals.