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 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.-- Read more... Abstract: 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. In spherically symmetric Finsler geometry, we find many nice examples with special curvature properties using PDE technique. Read more... 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.-- Provided by publisher Front Matter ....Pages i-xiii Spherically Symmetric Finsler Metrics (Enli Guo, Xiaohuan Mo)....Pages 1-8 Dually Flat Spherically Symmetric Metrics (Enli Guo, Xiaohuan Mo)....Pages 9-41 Spherically Symmetric Metrics of Isotropic Berwald Curvature (Enli Guo, Xiaohuan Mo)....Pages 43-54 Spherically Symmetric Douglas Metrics (Enli Guo, Xiaohuan Mo)....Pages 55-65 Projectively Flat Spherically Symmetric Metrics (Enli Guo, Xiaohuan Mo)....Pages 67-79 Spherically Symmetric Metrics of Scalar Curvature (Enli Guo, Xiaohuan Mo)....Pages 81-91 Spherically Symmetric Metrics of Constant Flag Curvature (Enli Guo, Xiaohuan Mo)....Pages 93-128 Spherically Symmetric W-Quadratic Metrics (Enli Guo, Xiaohuan Mo)....Pages 129-146 Back Matter ....Pages 147-154