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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- 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
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