一个完整的升降机为semisprays
A complete lift for semisprays
摘要：
在本文中，我们定义了一个完全提升的半粒子。如果$S$是流形$M$上的一个半映射，则它的完全提升是$TM$上的一个新的半映射$S^c$。这种提升的动机是双重的：首先，$S^c$的测地线对应于$S$的雅可比场，其次，这种完全提升推广和统一了以前已知的黎曼度量、仿射联络和正则拉格朗日的完全提升。当$S$是喷雾时，证明了$S^c$的射影几何唯一决定$S$ .我们还研究了如何对称性和运动的$S$升降机常数为对称性和运动的$S^c$。
英文摘要：
In this paper, we define a complete lift for semisprays. If $S$ is a semispray on a manifold $M$, its complete lift is a new semispray $S^c$ on $TM$. The motivation for this lift is two-fold: First, geodesics for $S^c$ correspond to the Jacobi fields for $S$, and second, this complete lift generalizes and unifies previously known complete lifts for Riemannian metrics, affine connections, and regular Lagrangians. When $S$ is a spray, we prove that the projective geometry of $S^c$ uniquely determines $S$. We also study how symmetries and constants of motions for $S$ lift into symmetries and constants of motions for $S^c$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
