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对某些黎曼-芬斯勒空间变换的研究:芬斯勒几何中的某些变换(英文)

对某些黎曼-芬斯勒空间变换的研究:芬斯勒几何中的某些变换(英文)

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2星价¥25.5 定价¥38.0
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  • ISBN:9787576701197
  • 装帧:一般胶版纸
  • 册数:暂无
  • 重量:暂无
  • 开本:其他
  • 页数:171
  • 出版时间:2022-07-01
  • 条形码:9787576701197 ; 978-7-5767-0119-7

内容简介

本书是一部有别于古典微分几何(苏步青先生研究的那些)的近代微分几何专著。本书的目标是研究黎曼一芬斯勒空间的某些变换比如,兰德斯空间可以看作是黎曼空间的变形。对更一般的情况而言,具有(α,β)一度量的芬斯勒空间可被视为黎曼空间的变形.为避免引用之前的黎曼一芬斯勒几何的知识,我们有了第1章,其中包含了有关黎曼一芬斯勒几何的概念和结果,在本书的其余部分中也使用了这些概念和结果。

目录

Preface 1 Introduction 1.1 Historical Development of Finsler Geometry 1.2 The Geometry of Finsler Spaces 1.3 Review of Literature about Finsler Geometry 1.4 Connections and Covariant Differentiations 1.5 Flag curvature and S-curvature in Finsler geometry 1.6 Some special Finsler spaces 1.7 KCC theory 1.8 Mathematical Cosmology in Finslerian space-time 2 On Finsler space with a special (α, β)-metric 2.1 Introduction 2.2 The condition to be a Berwald space 2.3 The condition to be a Douglas space 2.4 The condition to be a Weakly-Berwald space 3 On Randers change of a Finsler space with m-th root metric 3.1 Introduction 3.2 Preliminaries 3.3 Fundamental metric tensor of Randers transformed m-th root metric 3.4 Spray coefficients of Randers transformed m-th root metric 3.5 Conformally related Randers transformed m-th root metric 3.6 Locally dually flatness of Randers transformed m-th root metric 4 On Conformal Transformation of m-th root Finsler metric 4.1 Introduction 4.2 Preliminaries 4.3 Fundamental tensor and Spray coefficients of conformally trans-formed m-th root metric 4.4 Locally dually flat conformally transformed m-th root metric 4.5 Conformally transformed Einstein m-th root metric 4.6 Conformally transformed m-th root metric with Isotropic E-curvature 5 Transformation of a Finsler Space by Normalised Semi-Parallel Vector Fields 5.1 Introduction 5.2 Transformed Finsler space obtained by Normalised semi-parallel vector fields 5.3 Special Finsler spaces with semi-parallel vector fields 6 Predator-prey model with prey refuges: Jacobi stability vs Linear stability 6.1 Introduction 6.2 Preliminary 6.3 Applications of geometric theory to second order system 6.4 Mathematical models 6.5 Numerical simulations and discussion 6.6 Conclusions 7 Finsler-Randers Cosmological models in Modified Gravity Theories 7.1 Introduction 7.2 Finsler-Randers Cosmological Model in Einstein Theory 7.3 Fiusler-Randers cosmological model in Lyra geometry 7.4 Finsler-Randers Cosmological Model in General Class of Scalar-tensor theory 7.5 Finsler-Randers Cosmological Model in C-field theory 7.6 Conclusions Bibliography 编辑手记
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