Introduction

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

A chapter in Differential Geometry of Spray and Finsler Spaces, 2001, pp 1-2 from Springer

Abstract: Abstract In this book we study sprays and Finsler metrics. Roughly speaking, a spray on a manifold consists of compatible systems of second-order ordinary differential equations. A Finsler metric on a manifold is a family of norms in tangent spaces, which vary smoothly with the base point. Every Finsler metric determines a spray by its systems of geodesic equations. Thus, Finsler spaces can be viewed as special spray spaces. On the other hand, every Finsler metric defines a distance function by the length of minimial curves. Thus Finsler spaces can be viewed as regular metric spaces. Riemannian spaces are special regular metric spaces.

Keywords: Constant Curvature; Projective Geometry; Riemannian Space; Riemannian Metrics; Riemann Curvature (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_1

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DOI: 10.1007/978-94-015-9727-2_1

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