芬斯勒几何就是在度量上没有二次型限制的黎曼几何。它经陈省身先生大力提倡，近二十多年取得了蓬勃发展。S曲率是一个非常重要的非黎曼几何量，它无论在局部还是整体芬斯几何中都占有很重要的地位。S曲率是沈忠民教授为研究芬斯勒几何中的体积比较定理而引入的。广义(alpha,beta)度量是既丰富又重要的一类芬斯勒度量，它们包含(alpha,beta)度量、球对称度量、R. Bryant构造的部分度量和部分广义m次根度量等。因此，广义(alpha,beta)度量构成了很大一类芬斯勒度量，这有利于找出更多具有很好性质的芬斯勒度量。本项目拟以具有迷向S曲率的广义(alpha,beta)度量为研究对象，利用李群和偏微分方程的理论，通过beta形变的方法，借助Maple研究具有迷向S曲率的广义(alpha,beta)度量的局部结构。我们旨在刻划和分类此类度量。本项目的实施将促进国内外局部和整体芬斯勒几何的发展。

Finsler geometry is just the Riemannian geometry without the quadratic restriction on the metric. The rapid progress of Riemann-Finsler geometry has been made after the great encouragement of Professor S. S. Chern. The S-curvature is a very important non-Riemannian geometric quantity and plays an important role both in local and global Finsler geometry. It was introduced by Z. Shen to derive a volume comparison theorem in Riemann-Finsler geometry. General (alpha,beta)-metrics form a rich and important class of metrics. They include(alpha,beta)-metrics, spherically symmetric Finsler metrics, part of Bryant's metrics and part of general m-th root metrics and etc. Therefore, general (alpha,beta)-metrics make up of a much large class of Finsler metrics, which make it possible to find out more Finsler metrics to be of great properties. This project mainly focuses on general (alpha,beta)-metrics with isotropic S-curvature. By making use of the theory of Lie Groups and Partial Differential Equations and the method of beta deformations, we will study the local structure of general (alpha,beta)-metrics with isotropic S-curvature with the help of Maple. The main aim of this project is to characterize and classify this class of metrics. It will contribute to making rapid progress of local and global Finsler geometry.