芬斯勒幾何

內(nèi)容概要

this book exclusively deals with a special class of
Finsler metricsRandersmetrics．which are defined as the sum of a
Riemannian metric and a l一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．
 Xinyue Cheng is a Professor at the School of Mathematics and
Statistics ofChongqing University of Technology，China．Zhongmin Shen
is a Professor atthe Department ofMathematical Sciences ofIndiana
University Purdue University，TISA

書(shū)籍目錄

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 i0 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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