| preface to the second edition perface to the revised printing perface to the first edition ⅰ manifolds, tensors, and exterior forms 1 manifolds and vector fields 2 tensors and exterior forms 3 integration of differential forms 4 the lie derivative 5 the poincaré lemma and potentials 6 holonomic and nonholonomic constraints ⅱ geometry and topology 7 r3 and minkowski space 8 the geometry of surfaces in r3 9 covariant differentiation and curvature 10 geodesics 11 relativity, tensors, and curvature 12 curvature and topology: synge’s theorem 13 betti numbers and de rham’s theorem 14 harmonic forms ⅲ lie groups, bundles, and chern forms . 15 lie groups 16 vector bundles in geometry and physics 17 fiber bundles, gauss\ |
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