Finsler流形上的Killing对称性
Killing Symmetry on Finsler Manifold
摘要：
在Finsler流形上定义了Killing向量场$K$.利用Killing非线性1-形式$K^\flat$和Finsler非线性联络的喷雾算子$δ$，将Killing对称性简单地表示为$δK^\flat =0$. $K^\flat$与Finsler流形上Killing张量的推广有关，条件$δK^\flat =0$给出了求高阶导数守恒量的分析方法，这些守恒量可称为隐守恒量。我们展示了两个例子：克尔时空中的卡特常数和牛顿引力中的朗格-伦茨矢量。
英文摘要：
Killing vector fields $K$ are defined on Finsler manifold. The Killing symmetry is reformulated simply as $δK^\flat =0$ by using the Killing non-linear 1-form $K^\flat$ and the spray operator $δ$ with the Finsler non-linear connection. $K^\flat$ is related to the generalization of Killing tensors on Finsler manifold, and the condition $δK^\flat =0$ gives an analytical method of finding higher derivative conserved quantities, which may be called hidden conserved quantities. We show two examples: the Carter constant on Kerr spacetime and the Runge-Lentz vectors in Newtonian gravity.
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