Vll l Contents CHAPTER IV. Bundles and Connections 16. Derivations on the Algebra of Differential Forms 17. Fiber Bundles and Connections 18. Principal Fiber Bundles and G-Bundles 19. Principal and Induced Connections 20. Characteristic Classes 21. Jets CHAPTER V. Riemann Manifolds 22. Pseudo-Riemann Metrics and Covariant Derivatives 23. Geometry of Geodesies 24. Parallel Transport and Curvature 25. Computing with Adapted Frames and Examples 26. Riemann Immersions and Submersions 27. Jacobi Fields CHAPTER VI. Isometric Group Actions or Riemann G-Manifolds 28. Isometries, Homogeneous Manifolds, and Symmetric Spaces 29. Riemann G-Manifolds 30. Polar Actions CHAPTER VII. Symplectic and Poisson Geometry 31. Symplectic Geometry and Classical Mechanics 32. Completely Integrable Hamiltonian Systems 33. Poisson Manifolds 34. Hamiltonian Group Actions and Momentum Mappings List of Symbols Bibliography Index
Previous Page Next Page