《Finsler几何——从Randers空间进入(英文版)》是作者程新跃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。

《Finsler Geometry An Approach via Randers Spaces》is written by the Xinyue Chen and Zhongmin Shen.

《Finsler Geometry An Approach via Randers Spaces》 exclusively deals with a special class of Finsler metrics--Randersmetrics．which are defined as the sum of a Riemannian metric and a 1-form．Randers metrics derive from the research on General Relativity Theory andhavebeen applied in many areas of the natural sciences．They can also be naturallydeduced as the solution of the Zermelo navigation problem．The book providesreaders not only with essential findings on Randers metrics but also the core ideasand methods which are useful in Finsler geometry．It will be of significant interestto researchers and practitioners working in Finsler geometry，even in differentialgeometry or related natural fields．

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 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 CurvatureProperties

　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 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 FlagCurvature

　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 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