Generalized Sprays and Nonlinear Connections

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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.
22 pages + title page, 2 eps figures, 1 LaTeX picture

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Differential Geometry, 53C15 primary 53C22,58E10 secondary

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http://salesiana.dossiersoluciones.com/handle/123456789/66993

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0304067
 http://arxiv.org/abs/math/0304067

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arXiv