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内容大纲
本书是一部版权引进的英文版微分几何专著,中文书名可译为《芬斯勒几何的某些问题》。本书的作者为曼尼斯。库玛·古普塔(印度人),他在很多国家杂志和国际杂志上面发表了研究论文,据作者前言中所介绍:本书包含7章,每章又有许多部分,十进制表示法已用于方程式的编号之中。本书对方程的引用采用的形式,其中C,S和E分别代表相应的章节、部分和方程。 -
作者介绍
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目录
Preface
1 Introduction
1.1 Development of Finsler geometry
1.2 Finsler space
1.3 Metric tensor
1.4 Tangent space and its dual space
1.5 Magnitude of a vector; the notion of orthogonality
1.6 Cartan tensor and the generalized Christoffel symbols
1.7 Finsler connections
1.8 Projective transformation
1.9 Special Finsler spaces
1.10 Finslerian subspace
1.11 Finslerian hypersurface
2 On a four dimensional Finsler space
2.1 Introduction
2.2 Orthonormal frame and connection vectors
2.3 Scalar derivatives
2.4 Main scalars
2.5 Berwald space
2.6 Landsberg space
2.7 T-condition
2.8 v-curvature tensor
2.9 h-curvature tensor
2.10 Space of scalar curvature
3 Hypersurface of a four dimensional Finsler space
3.1 Introduction
3.2 Finslerian hypersurface
3.3 Main scalars of a four dimensional Finsler space and its hypersurface
3.4 C-reducible Finsler space
4 On subspaces and hypersurface of a Finsler space with metric given by an h-vector
4.1 Introduction.
4.2 The Finsler space *Fn = (Mn, *L)
4.3 Subspace *Fm of the Finsler space *Fn
4.4 Hypersurface *Fn-1 of Finsler space *Fn
5 On subspaces and hypersurface of a Finsler space with Randers conformal metric
5.1 Introduction.
5.2 The Finsler space *Fn = (Mn, *L)
5.3 Finsler subspaces given by Randers conformal change
5.4 Finslerian hypersurface given by Randers conformal metric
6 Hypersurfaces of h-conformally related Finsler spaces
6.1 Introduction
6.2 h-Conformal Finsler space
6.3 Hypersurface of an h-conformal Finsler space
7 On a projective mapping and Berwald h-recurrent Finsler connection
7.1 Introduction
7.2 Berwald h-recurrent connection
7.3 Condition for the Berwald connection of a Finsler space to be Berwald h-recurrent connection of another Finsler space 96
7.4 Projectively related spaces
7.5 Space of scalar curvature
7.6 Space of constant curvature
7.7 Space of zero curvature
7.8 A special projective mapping
Bibliography
编辑手记
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