The Geometry of Spherically Symmetric Finsler Manifolds, 1st ed. 2018 SpringerBriefs in Mathematics Series

Langue : Anglais

Auteurs : Guo Enli, Mo Xiaohuan

Couverture de l’ouvrage The Geometry of Spherically Symmetric Finsler Manifolds

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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.

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.

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