Homogeneous Finsler Spaces

  • Shaoqiang Deng

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Shaoqiang Deng
    Pages 1-29
  3. Shaoqiang Deng
    Pages 31-58
  4. Shaoqiang Deng
    Pages 59-77
  5. Shaoqiang Deng
    Pages 79-104
  6. Shaoqiang Deng
    Pages 105-133
  7. Shaoqiang Deng
    Pages 135-171
  8. Shaoqiang Deng
    Pages 173-228
  9. Back Matter
    Pages 229-240

About this book

Introduction

This book is a unique addition to the existing literature in the field of Finsler geometry. This is the first monograph to deal exclusively with homogeneous Finsler geometry and to make serious use of Lie theory in the study of this rapidly developing field. The increasing activity in Finsler geometry can be attested in large part to the driving influence of S.S. Chern, its proven use in many fields of scientific study such as relativity, optics, geosciences, mathematical biology, and psychology, and its promising reach to real-world applications.  This work has potential for broad readership; it is a valuable resource not only for specialists of Finsler geometry, but also for differential geometers who are familiar with Lie theory, transformation groups, and homogeneous spaces. The exposition is rigorous, yet gently engages the reader—student and researcher alike—in developing a ground level understanding of the subject. A one-term graduate course in differential geometry and elementary topology are prerequisites.

In order to enhance understanding, the author gives a detailed introduction and motivation for the topics of each chapter, as well as historical aspects of the subject, numerous well-selected examples, and thoroughly proved main results. Comments for potential further development are presented in Chapters 3–7.   A basic introduction to Finsler geometry is included in Chapter 1;  the essentials of the related classical theory of Lie groups, homogeneous spaces and groups of isometries are presented in Chapters 2–3. Then the author develops the theory of homogeneous spaces within the Finslerian framework. Chapters 4–6 deal with homogeneous, symmetric and weakly symmetric  Finsler spaces. Chapter 7  is entirely devoted to homogeneous Randers spaces,  which are good candidates for real world applications and beautiful illustrators of the developed theory.

Keywords

Finsler geometry Killing vector fields Lie theory Myers-Steenrod Theorem Randers spaces isometry groups

Authors and affiliations

  • Shaoqiang Deng
    • 1
  1. 1., School of Mathematical Sceinces & LPMCNankai UniversityTianjinChina, People's Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4614-4244-8
  • Copyright Information Springer Science+Business Media New York 2012
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4614-4243-1
  • Online ISBN 978-1-4614-4244-8
  • Series Print ISSN 1439-7382
  • About this book
Industry Sectors
Aerospace
Oil, Gas & Geosciences