Abstract
In this chapter, we will introduce an important geometric structure on a manifold and discuss some basic properties. Roughly speaking, a spray on a manifold M is a family of compatible systems of 2nd order ordinary differential equations in local coordinates
where (c i(t)) denotes the coordinates of a curve c(t),and G i(y) are positively homogeneous functions of degree two, i.e.,
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media Dordrecht
About this chapter
Cite this chapter
Shen, Z. (2001). Spray Spaces. In: Differential Geometry of Spray and Finsler Spaces. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9727-2_5
Download citation
DOI: https://doi.org/10.1007/978-94-015-9727-2_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-5673-3
Online ISBN: 978-94-015-9727-2
eBook Packages: Springer Book Archive