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
