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Abstract: In this paper, we define a complete lift for semisprays. If $S$ is asemispray 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 liftgeneralizes and unifies previously known complete lifts for Riemannian metrics,affine connections, and regular Lagrangians. When $S$ is a spray, we prove thatthe projective geometry of $S^c$ uniquely determines $S$. We also study howsymmetries and constants of motions for $S$ lift into symmetries and constantsof motions for $S^c$.



Author: Ioan Bucataru, Matias F. Dahl

Source: https://arxiv.org/



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