VARIATIONS, GEOMETRY AND PHYSICS -- VARIATIONS,GEOMETRYANDPHYSICS -- Contents -- Preface -- Part I VARIATIONAL PRINCIPLES ON JETBUNDLES -- Part III DIFFERENTIAL EQUATIONS ANDGEOMETRICAL STRUCTURES -- REMARKS ON THE HISTORY OF THE NOTIONOF LIE DIFFERENTIATION -- References -- SECOND-ORDER DIFFERENTIAL EQUATION FIELDSWITH SYMMETRY∗ -- Abstract -- 1. Introduction -- 2. The First-Order Case -- 2.1. Reduction -- 2.2. Reconstruction -- 3. The Second-Order Case -- 3.1. Reduction -- 3.2. Reconstruction -- 4. Lagrangian Systems -- 4.1. Lagrange-Poincaré Reduction -- 4.2. Routh's Procedure -- 4.3. Reconstruction -- 5. An Example: Wong's Equations -- Acknowledgement -- References -- DIMENSIONAL REDUCTION OFCURVATURE-DEPENDENT CENTRAL POTENTIALSON SPACES OF CONSTANT CURVATURE -- Abstract -- 1. Introduction and Motivation -- 2. Tagged Trigonometric Functions -- 3. Central Potentials in 3d Constant Curvature Manifolds -- 5. Final Comments -- Acknowledgement -- References -- DIRECT GEOMETRICAL METHODIN FINSLER GEOMETRY -- I. Minkowski Angle and Related Problems -- Introduction -- 1. Angle in Minkowski and Finsler Spaces -- 2. Diffeomorphisms which Keep Angle and Area -- 3. Deviation of Finsler Spaces from Riemannian Spaces -- II. Isometry between Finsler Spaces -- Introduction -- 4. Decomposition of the Base Manifold -- 5. Affine Deformation of a Finsler Space -- 6. 1-Parameter Continuous Group of Motions -- 7. Isometries between Finsler Spaces -- 8. Analytical Condition -- References -- LINEAR CONNECTIONS ALONG THE TANGENTBUNDLE PROJECTION -- Abstract -- 1. Introduction -- 2. Elements of the Calculus of Forms Along ˝ -- 3. The Case of a Bsode Connection -- 4. Linear Connections Along ˝ -- 5. A Variety of Related Connections -- 6. Torsion and Curvature of the Linear D Along ˝ -- 7. Variationality versus Metrizability.

8. Hessian Metrics Along ˝ and Finsler Spaces -- 9. Concluding Remarks -- ON THE INVERSE PROBLEMFOR AUTOPARALLELS∗ -- Abstract -- 1. The Inverse Problem in the Calculus of Variationsand Finsler Geometry -- 2. The Geometry of SODEs -- 3. The Helmholtz Conditions and the Finsler Inverse Problem -- 4. Remarks -- Acknowledgements -- References -- Part IV APPENDIX -- DEMETER KRUPKA -- List of publications, to December 2007 -- INDEX.