Abstract
Nonlinear connections and direction connections are two types of connections arising in Finsler geometry. In his work on generalized sprays, P. Dazord showed that there is a relationship between these two types (nonlinear connections were called sections by him). This relationship has also been used by J. Grifone in a work on prolongation of direction connections. In this paper we examine this relationship in a general setting. In particular, we show that E. Cartan’s condition “D” is necessary and sufficient for a direction connection to define a nonlinear one. Also, we prove a nonuniqueness result for direction connections associated to a given nonlinear one.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
