The Differential Geometry of Finsler Spaces

  • Hanno Rund

Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 101)

Table of contents

  1. Front Matter
    Pages II-XV
  2. Hanno Rund
    Pages 44-64
  3. Hanno Rund
    Pages 94-149
  4. Hanno Rund
    Pages 150-214
  5. Hanno Rund
    Pages 215-262
  6. Back Matter
    Pages 262-284

About this book

Introduction

The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduction to a branch of differential geometry which is closely related to various topics in theoretical physics, notably analytical dynamics and geometrical optics. With this second object in mind, an attempt has been made to describe the basic aspects of the theory in some detail - even at the expense of conciseness - while in the more specialised sections of the later chapters, which might be of interest chiefly to the specialist, a more succinct style has been adopted. The fact that there exist several fundamentally different points of view with regard to Finsler geometry has rendered the task of writing a coherent account a rather difficult one. This remark is relevant not only to the development of the subject on the basis of the tensor calculus, but is applicable in an even wider sense. The extensive work of H. BUSEMANN has opened up new avenues of approach to Finsler geometry which are independent of the methods of classical tensor analysis. In the latter sense, therefore, a full description of this approach does not fall within the scope of this treatise, although its fundamental l significance cannot be doubted.

Keywords

Finsler geometry Tensor calculus differential geometry geometry tensor analysis

Authors and affiliations

  • Hanno Rund
    • 1
  1. 1.The University of NatalBrazil

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-51610-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 1959
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-51612-2
  • Online ISBN 978-3-642-51610-8
  • Series Print ISSN 0072-7830
  • About this book