1 Introduction
1.1 Historical development from Geometry to Finsler Geometry
1.1.1 Origin of Geometry
1.1.2 Euclidean and Riemannian geometryFinsler Geometry
1.2 Differentiable Manifolds
1.2.1 n-dimensional Topological manifold
1.3 Curve and Line Element
1.4 Finsler Space
1.5 Physical motivation
1.6 .Tangent Space, Indicatrix and Minkowskian Space
1.6.1 Tangent Space
1.6.2 Indicatrix
1.6.3 Minkowskian Space
1.7 Finsler connections
1.7.1 Cartan's Connection
1.7.2 Rund's Connection
1.7.3 Berwald's connection
1.7.4 Hashiguchi's connection
1.8 Special Finsler Spaces
1.8.1 Definitions of some special Finsler spaces
1.8.2 Finsler space with (a, β)-metric
1.8.3 Finsler space with (Y, β)-metric
1.9 Intrinsic fields of orthonormal frames
1.9.1 Two-dimensional Finsler space
1.9.2 Three-dimensional Finsler space
1.9.3 Four-dimensional Finsler space
2 Generalized C"-Reducible Finsler Space
2.1 Introduction
2.2 Basic concept of generalized Cv-Reducible Finsler Space offirst kind
2.3 Generalized C”-Reducible Finsler Space of type Ⅰ
2.4 Generalized C"-Reducible Finsler Space of type Ⅱ
2.5 Basic concept of generalized Cv-Reducible Finsler Space ofsecond kind
2.6 Generalized Cv-Reducible Finsler Space of type Ⅲ
2.7 Generalized Cv-Reducible Finsler Space of type Ⅳ
3 On Finsler space with generalized (a, β)-Metric
3.1 Introduction
3.2 Preliminaries
3.3 Berwald frame for Two-dimensional generalized (a, B)-Metric
3.4 Main scalar of Two-dimensional generalized (a, B)-metric
3.5 Landsberg and Berwald spaces with generalized (a, B)-Metric
3.6 Landsberg and Berwald spaces with m-generalized Kropina metric
4 On Finsler spaces with unified main scalar (LC) is of theform L2C2 =f(y)+g(x)
4.1 Introduction
4.2 The condition L2C2 = f(y) + g(x)
4.3 Landsberg and Berwald spaces satisfying the condition L2C2 –f(y)+g(x)
5 On Finsler space with h-Randers conformal change
5.1 Introduction
5.2 Cartan's connection of Fn
5.3 Some properties of h-Randers conformal change
5.4 Geodesic Spray coefficients of Fn
5.5 C-reducibilty of Fn
5.6 Some Important tensors of Fn
6 Three-Dimensional Conformally flat Finsler Spaces
6.1 Introduction
6.2 Preliminaries
6.3 The scalar curvature R of the Finsler space (M，L)
7 On Finsler spaces with (Y,B)-Metric
7.1 Preliminaries
7.2 Introduction
7.3 Basic tensors of (y, B)-metric
7.4 Important tensors of (Y,B)-metric
7.5 Berwald Frame for Two-dimensional (Y, B) -Metric
7.6 Main Scalar of Two-dimensional (Y, B) -Metric
7.7 Geodesic of a Finsler space with (Y, B)-metric
7.8 Berwald connection for a Finsler space with (Y, B)-metric
7.9 Scalar curvature of a two-dimensional Finsler space with (Y, B) metric
7.10 Lagrange spaces with (Y, β)-metric
7.11 The fundamental tensor of a Lagrange space with (Y, B)-Metric
7.12 Eular-Lagrange equations in Lagrange spaces with (Y,B)-Metric
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