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The Geometry of Spherically Symmetric Finsler Manifolds

  • Book
  • © 2018

Overview

Authors:
  1. Enli Guo

    1. College of Applied Sciences, Beijing University of Technology, Beijing, China

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    You can also search for this author in PubMed   Google Scholar

  2. Xiaohuan Mo

    1. School of Mathematical Sciences, Peking University, Beijing, China

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    You can also search for this author in PubMed   Google Scholar

  • Provides broader examples of Finsler metrics with nice curvature properties
  • Establishes a lot of beautiful classification theorems
  • Presents PDE method to study Riemann-Finsler geometry

Part of the book series: SpringerBriefs in Mathematics (BRIEFSMATH)

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Table of contents (8 chapters)

  1. Front Matter

    Pages i-xiii
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  2. Spherically Symmetric Finsler Metrics

    • Enli Guo, Xiaohuan Mo
    Pages 1-8

  3. Dually Flat Spherically Symmetric Metrics

    • Enli Guo, Xiaohuan Mo
    Pages 9-41

  4. Spherically Symmetric Metrics of Isotropic Berwald Curvature

    • Enli Guo, Xiaohuan Mo
    Pages 43-54

  5. Spherically Symmetric Douglas Metrics

    • Enli Guo, Xiaohuan Mo
    Pages 55-65

  6. Projectively Flat Spherically Symmetric Metrics

    • Enli Guo, Xiaohuan Mo
    Pages 67-79

  7. Spherically Symmetric Metrics of Scalar Curvature

    • Enli Guo, Xiaohuan Mo
    Pages 81-91

  8. Spherically Symmetric Metrics of Constant Flag Curvature

    • Enli Guo, Xiaohuan Mo
    Pages 93-128

  9. Spherically Symmetric W-Quadratic Metrics

    • Enli Guo, Xiaohuan Mo
    Pages 129-146

  10. Back Matter

    Pages 147-154
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Keywords

About this book

This book presents properties, examples, rigidity theorems and classification results of such Finsler metrics. In particular, this book introduces how to investigate spherically symmetric Finsler geometry using ODE or PDE methods. Spherically symmetric Finsler geometry is a subject that concerns domains in R^n with spherically symmetric metrics.

Recently, a significant progress has been made in studying Riemannian-Finsler geometry. However, constructing nice examples of Finsler metrics turn out to be very difficult. In spherically symmetric Finsler geometry, we find many nice examples with special curvature properties using PDE technique. The studying of spherically symmetric geometry shows closed relation among geometry, group and equation.

Reviews

“The exposition is very comprehensive for the reader and this certainly should become a good reference book for beginners in Finsler geometry.” (Libing Huang, Mathematical Reviews, August, 2019)

Authors and Affiliations

  • College of Applied Sciences, Beijing University of Technology, Beijing, China

    Enli Guo

  • School of Mathematical Sciences, Peking University, Beijing, China

    Xiaohuan Mo

Bibliographic Information

  • Book Title: The Geometry of Spherically Symmetric Finsler Manifolds

  • Authors: Enli Guo, Xiaohuan Mo

  • Series Title: SpringerBriefs in Mathematics

  • DOI: https://doi.org/10.1007/978-981-13-1598-5

  • Publisher: Springer Singapore

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

  • Copyright Information: The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd., part of Springer Nature 2018

  • Softcover ISBN: 978-981-13-1597-8Published: 11 October 2018

  • eBook ISBN: 978-981-13-1598-5Published: 21 September 2018

  • Series ISSN: 2191-8198

  • Series E-ISSN: 2191-8201

  • Edition Number: 1

  • Number of Pages: XIII, 154

  • Number of Illustrations: 6 b/w illustrations

  • Topics: Differential Geometry, Global Analysis and Analysis on Manifolds

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