Finsler几何 : 从Randers空间进入
出版社：科学出版社
年代：2011
定价：70.0
书籍简介:
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。
书籍目录:
Chapter 1 Randers Spaces1.1 Randers Norms1.2 Distortion and Volume Form1.3 Caftan Torsion1.4 DualityBibliographyChapter 2 Randers Metrics and Geodesics2.1 Randers Metrics2.2 Zermelo's Navigation Problem2.3 Geodesics2.4 Randers Metrics of Berwald TypeBibliographyChapter 3 Randers Metrics of Isotropic S-Curvature3.1 S-Curvature3.2 Isotropic S-Curvature in Terms of a and/33.3 Isotropic S-Curvature in Terms of h and W3.4 Examples of Isotropic S-Curvature3.5 Randers Metrics with Secondary Isotropic S-CurvatureBibliographyChapter 4 Riemann Curvature and Ricci Curvature4.1 Definitions4.2 Riemann Curvature of Randers Metrics4.3 Randers Metrics of Scalar Flag CurvatureBibliographyChapter 5 Projective Geometry of Randers Spaces5.1 Projective Quantities5.2 Douglas-Randers Metrics5.3 Weyl-Randers Metrics5.4 Generalized Douglas Weyl Randers MetricsBibliographyChapter 6 Randers Metrics with Special Riemann CurvatureProperties6.1 Ricci-Quadratic Randers Metrics6.2 Randers Metrics of R-Quadratic Curvature6.3 Randers Metrics of W-Quadratic Curvature6.4 Randers Metrics of Sectional Flag CurvatureBibliographyChapter 7 Randers Metrics of Weakly Isotroplc Flag Curvature7.1 Weak Einstein Randers Metrics7.2 Randers Metrics of Weakly Isotropic Flag Curvature7.3 Solutions via Navigation7.4 Weak Einstein Randers Metrics via Navigation DataBibliographyChapter 8 Projectively Flat Randers Metrics8.1 Projectively Flat Randers Metrics of Constant Flag Curvature8.2 Projectively Flat Randers Metrics of Weakly Isotropic FlagCurvature8.3 Projeetively Flat Randers Metrics on SBibliographyChapter 9 Conformal Geometry of Randers Metrics9.1 Conformally Invariant Spray9.2 Conformally Flat Randers Metrics9.3 Conformally Berwaldian Randers MetricsBibliographyChapter 10 Dually Flat Randers Metrics10.1 Dually Flat Finsler Metrics10.2 Dually Flat Randers Metrics10.3 Dually Flat Randers Metrics with Isotropic S-CurvatureBibliographyIndex
内容摘要:
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 at the Department ofMathematical Sciences ofIndiana University Purdue University，TISA.
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