Spray Spaces

Zhongmin Shen ()
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Zhongmin Shen: Indiana University-Purdue University at Indianapolis, Department of Mathematical Sciences

Chapter Chapter 4 in Differential Geometry of Spray and Finsler Spaces, 2001, pp 47-61 from Springer

Abstract: 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 4.1 $${\ddot c^i} + 2{G^i}(\dot c) = 0$$ 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., $${G^i}\left( {\lambda y} \right) = {\lambda ^2}{G^i}\left( y \right),\quad \lambda > 0.$$

Keywords: Vector Field; Tangent Bundle; Integral Curve; Path Space; Finsler Space (search for similar items in EconPapers)
Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-94-015-9727-2_5

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DOI: 10.1007/978-94-015-9727-2_5

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