Author | Rund, Hanno. author |
---|---|
Title | The Differential Geometry of Finsler Spaces [electronic resource] / by Hanno Rund |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1959 |
Connect to | http://dx.doi.org/10.1007/978-3-642-51610-8 |
Descript | XV, 284 p. online resource |
I: Calculus of Variations. Minkowskian Spaces -- ยง 1. Problems in the calculus of variations in parametric form -- ยง 2. The tangent space. The indicatrix -- ยง 3. The metric tensor and the osculating indicatrix -- ยง 4. The dual tangent space. The figuratrix -- ยง 5. The Hamiltonian function -- ยง 6. The trigonometric functions and orthogonality -- ยง 7. Definitions of angle -- ยง 8. Area and Volume -- II: Geodesics: Covariant Differentiation -- ยง 1. The differential equations satisfied by the geodesics -- ยง 2. The explicit expression for the second derivatives in the differential equations of the geodesies -- ยง 3. The differential of a vector -- ยง 4. Partial differentiation of vectors -- ยง 5. Elementary properties of ?-differentiation -- III: The โEuclidean Connectionโ of E. Cartan -- ยง 1. The fundamental postulates of Cartan -- ยง 2. Properties of the covariant derivative -- ยง 3. The general geometry of paths: the connection of Berwald -- ยง 4. Further connections arising from the general geometry of paths -- ยง 5. The osculating Riemannian space -- ยง 6. Normal coordinates -- IV: The Theory of Curvature -- ยง 1. The commutation formulae -- ยง 2. Identities satisfied by the curvature tensors -- ยง 3. The Bianchi identities -- ยง4. Geodesic deviation Ill -- ยง 5. The first and second variations of the length integral -- ยง 6. The curvature tensors arising from Berwaldโs connection -- ยง 7. Spaces of constant curvature -- ยง 8. The projective curvature tensors -- V: The Theory of Subspaces -- ยง 1. The theory of curves -- ยง 2. The projection factors -- ยง 3. The induced connection parameters.; -- ยง 4. Fundamental aspects of the theory of subspaces based on the euclidean connection -- ยง 5. The Lie derivative and its application to the theory of subspaces -- ยง 6. Surfaces imbedded in an F3 -- ยง 7. Fundamental aspects of the theory of subspaces from the point of view of the locally Minkowskian metric -- ยง 8. The differential geometry of the indicatrix and the geometrical significance of the tensor Sijhk -- ยง 9. Comparison between the induced and the intrinsic connection parameters -- VI: Miscellaneous Topics -- ยง 1. Groups of motions -- ยง 2. Conformai geometry -- ยง 3. The equivalence problem -- ยง 4. The theory of non-linear connections -- ยง 5. The local imbedding theories -- ยง 6. Two-dimensional Finsler spaces -- Appendix: Bibliographical references to related topics -- Symbols