A COMPLETE LIFT FOR SEMISPRAYS

Author:

BUCATARU IOAN1,DAHL MATIAS F.2

Affiliation:

1. Faculty of Mathematics, Al.I.Cuza University, B-dul Carol 11, Iasi, 700506, Romania

2. Institute of Mathematics, P. O. Box 1100, 02015 Helsinki University of Technology, Finland

Abstract

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 Scon TM. The motivation for this lift is two-fold: First, geodesics for Sccorrespond 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 Scuniquely determines S. We also study how symmetries and constants of motions for S lift into symmetries and constants of motions for Sc.

Publisher

World Scientific Pub Co Pte Lt

Subject

Physics and Astronomy (miscellaneous)

Cited by 7 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Special coordinate systems in pseudo-Finsler geometry and the equivalence principle;Journal of Geometry and Physics;2017-04

2. Complete lift of vector fields and sprays to T∞M;International Journal of Geometric Methods in Modern Physics;2015-10-25

3. Connections on distributions and geodesic sprays;Russian Mathematics;2013-03-26

4. SYMMETRIES, NEWTONOID VECTOR FIELDS AND CONSERVATION LAWS IN THE LAGRANGIAN k-SYMPLECTIC FORMALISM;Reviews in Mathematical Physics;2012-11

5. k-parameter geodesic variations;Journal of Geometry and Physics;2012-11

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