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The Geometry of Spherically Symmetric Finsler Manifolds

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 dom...

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Bibliographic Details
Main Authors: Guo, Enli, Mo, Xiaohuan (Author)
Format: eBook
Language:English
Published: Singapore Springer Nature Singapore 2018, 2018
Edition:1st ed. 2018
Series:SpringerBriefs in Mathematics
Subjects:
Geometry, Differential
Manifolds (mathematics)
Differential Geometry
Global Analysis (mathematics)
Global Analysis And Analysis On Manifolds
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
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505 0 |a Chapter 1. Spherically Symmetric Finsler Metrics -- Chapter 2. Dually Flat Spherically Symmetric Metrics -- Chapter 3. Spherically Symmetric Metrics of Isotropic Berwald Curvature -- Chapter 4. Spherically Symmetric Douglas Metrics -- Chapter 5. Projectively Flat Spherically Symmetric Metrics -- Chapter 6. Spherically Symmetric Metrics of Scalar Curvature -- Chapter 7. Spherically Symmetric Metrics of Constant Flag Curvature -- Chapter 8. Spherically Symmetric W-quadratic Metrics. 
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653 |a Global Analysis and Analysis on Manifolds 
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520 |a 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 

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