The geometry of spherically symmetric Finsler manifolds

Description

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... Content: Spherically symmetric Finsler metrics -- Dually flat spherically symmetric metrics -- Spherically symmetric Douglas metrics -- Projectively flat spherically symmetric metrics -- Spherically symmetric metrics of scalar curvature -- Spherically symmetric metrics of constant flag curvature -- Spherically symmetric w-quadratic metrics.