The Differential Geometry of Finsler Spaces
The present monograph is motivated by two distinct aims. Firstly, an endeavour has been made to furnish a reasonably comprehensive account of the theory of Finsler spaces based on the methods of classical differential geometry. Secondly, it is hoped that this monograph may serve also as an introduct...
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| Format: | eBook |
| Language: | English |
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Berlin, Heidelberg
Springer Berlin Heidelberg
1959, 1959
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| Edition: | 1st ed. 1959 |
| Series: | Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- § 8. The differential geometry of the indicatrix and the geometrical significance of the tensor Sijhk
- § 9. Comparison between the induced and the intrinsic connection parameters
- VI: Miscellaneous Topics
- § 1. Groups of motions
- § 2. Conformai geometry
- § 3. The equivalence problem
- § 4. The theory of non-linear connections
- § 5. The local imbedding theories
- § 6. Two-dimensional Finsler spaces
- Appendix: Bibliographical references to related topics
- Symbols
- I: Calculus of Variations. Minkowskian Spaces
- § 1. Problems in the calculus of variations in parametric form
- § 2. The tangent space. The indicatrix
- § 3. The metric tensor and the osculating indicatrix
- § 4. The dual tangent space. The figuratrix
- § 5. The Hamiltonian function
- § 6. The trigonometric functions and orthogonality
- § 7. Definitions of angle
- § 8. Area and Volume
- II: Geodesics: Covariant Differentiation
- § 1. The differential equations satisfied by the geodesics
- § 2. The explicit expression for the second derivatives in the differential equations of the geodesies
- § 3. The differential of a vector
- § 4. Partial differentiation of vectors
- § 5. Elementary properties of ?-differentiation
- III: The “Euclidean Connection” of E. Cartan
- § 1. The fundamental postulates of Cartan
- § 2. Properties of the covariant derivative
- § 3. The general geometry of paths: the connection of Berwald
- § 4. Further connections arising from the general geometry of paths
- § 5. The osculating Riemannian space
- § 6. Normal coordinates
- IV: The Theory of Curvature
- § 1. The commutation formulae
- § 2. Identities satisfied by the curvature tensors
- § 3. The Bianchi identities
- §4. Geodesic deviation Ill
- § 5. The first and second variations of the length integral
- § 6. The curvature tensors arising from Berwald’s connection
- § 7. Spaces of constant curvature
- § 8. The projective curvature tensors
- V: The Theory of Subspaces
- § 1. The theory of curves
- § 2. The projection factors
- § 3. The induced connection parameters.;
- § 4. Fundamental aspects of the theory of subspaces based on the euclidean connection
- § 5. The Lie derivative and its application to the theory of subspaces
- § 6. Surfaces imbedded in anF3
- § 7. Fundamental aspects of the theory of subspaces from the point of view of the locally Minkowskian metric