本书系统地研究和讨论了一类自然而重要的芬斯勒度量-Randers度量。Randers度量来自于对广义相对论的研究，且已在包括生物学、电子显微镜理论等在内的众多自然科学领域中有深入应用。特别地，Randers度量可作为Zermelo导航术问题的解而自然地导出。由于Randers度量的特殊性，使得人们可以对其各种几何量作深入计算，深刻地揭示其几何性质。也正是由于对Randers度量的研究，深化了人们对芬斯勒度量几何性质的认识，极大地推动了芬斯勒几何的发展。所以，Randers空间的几何是芬斯勒几何的重要组成部分，在芬斯勒几何的发展进程中扮演着不可或缺的重要角色。本书是作者根据自己多年的研究积累，倾力写成的一本关于Randers空间几何的专著，也是国内外芬斯勒几何领域中第一部系统介绍Randers度量的著作。全书包含了作者近十年来在关于Randers度量的研究工作中取得的一系列重要成果，也包含了其他学者所取得的相关重要成果。本书系统而全面地展示了Randers空间几何在近年来取得的重要研究进展和对推动芬斯勒几何发展而发挥的重要作用，也自然地介绍了芬斯勒几何的有关重要理论和方法。全书内容新颖、丰富，结构严谨、自然，论述清新、流畅。
样章试读
目录
- Chapter 1 Randers Spaces
1.1 Randers Norms
1.2 Distortion and Volume Form
1.3 Cartan 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 α and β
3.3 Isotropic S-Curvature in Terms of h and W
3.4 Examples of Isotropic S-Curvature
3.5 Randers Metrics with Secondary Isotropic S-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 Riemann Curvature Properties
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 Isotropic Flag Curvature
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 Flag Curvature
8.2 Projectively Flat Randers Metrics of Weakly Isotropic Flag Curvature
8.3 Projectively Flat Randers Metrics on S^n
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 10 Dually Flat Randers Metrics
10.1 Dually Flat Finsler Metrics
10.2 Dually Flat Randers Metrics
10.3 Dually Flat Randers Metrics with Isotropic S-Curvature
Bibliography
Index
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