论文标题
将Eisenhart-Duval的升降机提升至最小的Brane
Lifting the Eisenhart-Duval Lift to a Minimal Brane
论文作者
论文摘要
在$ n $维构型空间上动态系统的运动可能被认为是以$（n+2）$尺寸时空移动的无效的null Geodsics的光阴影。在本文中，表明，如果配置空间为$ n $维的欧几里得空间，并且在没有磁性力的情况下，则可以将Eisenhart-Duval升降机视为$（n+1）$ - Brane在平坦的$（n+4）$（n+4）$（n+4）$两次的空间中移动。如果Eisenhart-Duval升降机是Ricci平坦的，则$（n+1）$ - Brane的移动以极大的时空体积的方式移动。 $ n $点粒子在其相互吸引力的影响下以三维欧几里得空间移动的$ n $点粒子的运动提供了一个惊人的例子。还构建了具有弯曲配置空间指标和速度依赖性力的嵌入。解决了两次引起的一些问题。
The motion of a dynamical system on an $n$-dimensional configuration space may be regarded as the lightlike shadow of null geodsics moving in an $(n+2)$ dimensional spacetime known as its Einsenhart-Duval lift. In this paper it is shown that if the configuration space is $n$-dimensional Euclidean space, and in the absence of magnetic type forces, the Eisenhart-Duval lift may be regarded as an $(n+1)$-brane moving in a flat $(n+4)$ -dimensional space with two times. If the Eisenhart-Duval lift is Ricci flat, then the $(n+1)$-brane moves in such a way as to extremise its spacetime volume. A striking example is provided by the motion of $N$ point particles moving in three-dimensional Euclidean space under the influence of their mutual gravitational attraction. Embeddings with curved configuration space metrics and velocity dependent forces are also be constructed. Some of the issues arising from the two times are addressed.
