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Homogeneous Finsler Spaces

  • Book
  • © 2012

Overview

Authors:
  1. Shaoqiang Deng

    1. , School of Mathematical Sceinces & LPMC, Nankai University, Tianjin, China, People's Republic

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  • Presents the most recent results on the applications of Lie theory to Finsler geometry
  • Provides an accessible introduction to Finsler geometry that allows the reader to quickly understand topics and to access related problems
  • Contains related work concerning Randers spaces, making it suitable for readers with a background in biology, as well as various topics for readers with backgrounds in pure algebra?
  • Includes supplementary material: sn.pub/extras
  • Includes supplementary material: sn.pub/extras

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

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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction to Finsler Geometry

    • Shaoqiang Deng
    Pages 1-29

  3. Lie Groups and Homogeneous Spaces

    • Shaoqiang Deng
    Pages 31-58

  4. The Group of Isometries

    • Shaoqiang Deng
    Pages 59-77

  5. Homogeneous Finsler Spaces

    • Shaoqiang Deng
    Pages 79-104

  6. Symmetric Finsler Spaces

    • Shaoqiang Deng
    Pages 105-133

  7. Weakly Symmetric Finsler Spaces

    • Shaoqiang Deng
    Pages 135-171

  8. Homogeneous Randers Spaces

    • Shaoqiang Deng
    Pages 173-228

  9. Back Matter

    Pages 229-240
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Keywords

About this book

Homogeneous Finsler Spaces is the first book to emphasize the relationship between Lie groups and Finsler geometry, and the first to show the validity in using Lie theory for the study of Finsler geometry problems. This book contains a series of new results obtained by the author and collaborators during the last decade. The topic of Finsler geometry has developed rapidly in recent years. One of the main reasons for its surge in development is its use in many scientific fields, such as general relativity, mathematical biology, and phycology (study of algae).  This monograph introduces the most recent developments in the study of Lie groups and homogeneous Finsler spaces,  leading the reader to directions for further development. The book contains many interesting results such as a Finslerian version of  the Myers-Steenrod Theorem, the existence theorem for invariant non-Riemannian Finsler metrics on coset spaces, the Berwaldian characterization of globally symmetric Finsler spaces, the construction of examples of reversible non-Berwaldian Finsler spaces with vanishing S-curvature, and a classification of homogeneous Randers spaces with isotropic S-curvature and positive flag curvature. Readers with some background in Lie theory or differential geometry can quickly begin studying problems concerning Lie groups and Finsler geometry.​

Reviews

From the reviews:

“The main purpose of this book is to show how ideas from Lie theory have spread to Finsler geometry. This book is the first one in the field of homogeneous Finsler spaces. … Finsler geometry has been developing rapidly, but this book may give a new spirit to Finsler geometry from the view of Lie theory, and it can be highly recommended to anyone who wants to study Finsler geometry from this point of view.” (Hamid Reza Salimi Moghaddam, Mathematical Reviews, June, 2013)

“The aim of the present book is to introduce the aspects of Finsler geometry that can be expressed in terms of Lie theory, having as permanent example the case of homogeneous/symmetric Riemannian manifolds. In this way, new very interesting facts are produced by non-Riemannian tools and geometrical objects like flag and S-curvature. … this book will be of great interest for a large number of geometers.” (Radu Miron, Zentralblatt MATH, Vol. 1253, 2013)

Authors and Affiliations

  • , School of Mathematical Sceinces & LPMC, Nankai University, Tianjin, China, People's Republic

    Shaoqiang Deng

Bibliographic Information

  • Book Title: Homogeneous Finsler Spaces

  • Authors: Shaoqiang Deng

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-1-4614-4244-8

  • Publisher: Springer New York, NY

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Science+Business Media New York 2012

  • Hardcover ISBN: 978-1-4614-4243-1Published: 01 August 2012

  • Softcover ISBN: 978-1-4899-9476-9Published: 19 September 2014

  • eBook ISBN: 978-1-4614-4244-8Published: 01 August 2012

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XIV, 242

  • Topics: Differential Geometry

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