Generalized Sprays and Nonlinear Connections
Differential Geometry
2007-05-23 v1
Abstract
The main purposes of this article are to extend our previous results on homogeneous sprays to arbitrary (generalized) sprays, to show that locally diffeomorphic exponential maps can be defined for any (generalized) spray, and to give a (possibly nonlinear) covariant derivative for any (possibly nonlinear) connection. In the process, we introduce vertically homogeneous connections. Unlike homogeneous connections, these allow us to include Finsler spaces among the applications. We provide significant support for the prospect of studying nonlinear connections via (generalized) sprays. One of the most important is our generalized APS correspondence.
Cite
@article{arxiv.math/0304067,
title = {Generalized Sprays and Nonlinear Connections},
author = {L. Del Riego and Phillip. E. Parker},
journal= {arXiv preprint arXiv:math/0304067},
year = {2007}
}
Comments
22 pages + title page, 2 eps figures, 1 LaTeX picture