芬斯勒几何：Randers空间方法（英文版）
作者：程新跃，沈忠民 著
出版时间：2011年版
内容简介
this book exclusively deals with a special class ofFinsler metricsRandersmetrics．which are defined as the sum of aRiemannian metric and a l一form．Randers metrics derive from theresearch on General Relativity Theory andhavebeen applied in manyareas of the natural sciences．They can also be naturallydeduced asthe solution of the Zermelo navigation problem．The bookprovidesreaders not only with essential findings on Randers metricsbut also the core ideasand methods which are useful in Finslergeometry．It will be of significant interestto researchers andpractitioners working in Finsler geometry，even indifferentialgeometry or related natural fields．Xinyue Cheng is a Professor at the School of Mathematics andStatistics ofChongqing University of Technology，China．Zhongmin Shenis a Professor atthe Department ofMathematical Sciences ofIndianaUniversity Purdue University，TISA
目录
Chapter 1 Randers Spaces
1.1 Randers Norms
1.2 Distortion and Volume Form
1.3 Caftan Torsion
1.4 Duality
Bibliography
Chapter 2 Randers Metrics and Geodesics
2.1 Randers Metrics
2.2 Zermelo's Navigation Problem
2.3 Geodesics
2.4 Randers Metrics of Berwald Type
Bibliography
Chapter 3 Randers Metrics of Isotropic S-Curvature
3.1 S-Curvature
3.2 Isotropic S-Curvature in Terms of a and/3
3.3 Isotropic S-Curvature in Terms of h and W
3.4 Examples of Isotropic S-Curvature
3.5 Randers Metrics with Secondary IsotropicS-Curvature
Bibliography
Chapter 4 Riemann Curvature and Ricci Curvature
4.1 Definitions
4.2 Riemann Curvature of Randers Metrics
4.3 Randers Metrics of Scalar Flag Curvature
Bibliography
Chapter 5 Projective Geometry of Randers Spaces
5.1 Projective Quantities
5.2 Douglas-Randers Metrics
5.3 Weyl-Randers Metrics
5.4 Generalized Douglas Weyl Randers Metrics
Bibliography
Chapter 6 Randers Metrics with Special RiemannCurvatureProperties
6.1 Ricci-Quadratic Randers Metrics
6.2 Randers Metrics of R-Quadratic Curvature
6.3 Randers Metrics of W-Quadratic Curvature
6.4 Randers Metrics of Sectional Flag Curvature
Bibliography
Chapter 7 Randers Metrics of Weakly Isotroplc FlagCurvature
7.1 Weak Einstein Randers Metrics
7.2 Randers Metrics of Weakly Isotropic Flag Curvature
7.3 Solutions via Navigation
7.4 Weak Einstein Randers Metrics via Navigation Data
Bibliography
Chapter 8 Projectively Flat Randers Metrics
8.1 Projectively Flat Randers Metrics of Constant FlagCurvature
8.2 Projectively Flat Randers Metrics of Weakly IsotropicFlagCurvature
8.3 Projeetively Flat Randers Metrics on S
Bibliography
Chapter 9 Conformal Geometry of Randers Metrics
9.1 Conformally Invariant Spray
9.2 Conformally Flat Randers Metrics
9.3 Conformally Berwaldian Randers Metrics
Bibliography
Chapter i0 Dually Flat Randers Metrics
10.1 Dually Flat Finsler Metrics
10.2 Dually Flat Randers Metrics
10.3 Dually Flat Randers Metrics with IsotropicS-Curvature
Bibliography
Index
