Preface. 1. The geometry of tangent bundle. 2. Finsler spaces. 3. Lagrange spaces. 4. The geometry of cotangent bundle. 5. Hamilton spaces. 6. Cartan spaces. 7. The duality between Lagrange and Hamilton spaces. 8. Symplectic transformations of the differential geometry of T* M. 9. The dual bundle of a k-osculator bundle. 10. Linear connections on the manifold T*2M. 11. Generalized Hamilton spaces of order 2. 12. Hamilton spaces of order 2. 13. Cartan spaces of order 2. Bibliography. Index.

The Geometry of Hamilton and Lagrange Spaces

In the paper, we study the shortest time problem on a Riemannian space with an external force. We show that such problem can be converted to a shortest path problem on a Randers space. By choosing an appropriate external force on the Euclidean space, we obtain a non-trivial Randers metric of zero flag curvature. We also show that any positively complete Randers metric with zero flag curvature must be locally Minkowskian.

Finsler Metrics with K= 0 and S= 0

Theory of Finsler spaces with (α, β)-metric

In Finsler geometry, there are infinitely many models of constant curvature. The Funk metrics, the Hilbert-Klein metrics and the Bryant metrics are projectively flat with non-zero constant curvature. A recent example constructed by the author is projectively flat with zero curvature. In this paper, we introduce a technique to construct non-projectively flat Finsler metrics with zero curvature in each dimension. The technique can be used to construct many non-projectively flat Finsler metrics of constant curvature.

Finsler Metrics with K=0 and S=0

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H. Yasuda

Papers

On Randers spaces of scalar curvature