| 统并深入地阐述了微分几何的概念及性质，并且全面研究了cartan联络，很适合研究生一年级学习理解 |
| 《微分几何(英文影印版)》 foreword note on the second printing preface 1 in the ashes of the ether: differential topology 1. smooth manifolds 2. submanifolds 3. fiber bundles 4. tangent vectors, bundles, and fields 5. differential forms 2 looking for the forest-in the leaves: foliations 1. integral curves 2. distributions 3. integrability conditions 4. the frobenius theorem 5. the frobenius theorem in terms of differential forms 6. foliations 7. leaf holonomy 8. simple foliations 3 the fundamental theorem of calculus .1. the maurer-cartan form 2. lie algebras 3. structural equation 4. adjoint action 5. the darboux derivative 6. the fundamental theorem: local version 7. the fundamental theorem: global version 8. monodromy and completeness 4 shapes fantastic: klein geometries 1. examples of planar klein geometries 2. principal bundles: characterization and reduction 3. klein geometries 4. a fundamental property 5. the tangent bundle of a klein geometry 6. the meteor tracking problem 7. the gauge view of klein geometries 5 shapes high fantastical: cartan geometries 1. the base definition of cartan geometries 2. the principal bundle hidden in a cartan geometry 3. the bundle definition of a cartan geometry 4. development, geometric orientation, and holonomy 5. flat cartan geometries and uniformization 6. cartan space forms 7. symmetric spaces 6 riemannian geometry 1. the model euclidean space 2. euclidean and riemannian geometry 3. the equivalence problem for riemannian metrics 4. riemannian space forms 5. subgeometry of a riemannian geometry 6. isoparametric submanifolds 7 msbius geometry 1. the msbius and weyl models 2. msbius and weyl geometries 3. equivalence problems for a conformal metric 4. submanifolds of msbius geometry 5. immersed curves 6. immersed surfaces 8 projective geometry 1. the projective model 2. projective cartan geometries 3. the geometry of geodesics 4. the projective connection in a riemannian geometry 5. a brief tour of projective geometry a ehresmann connections 1. the geometric origin of ehresmann connections 2. the reductive case 3. ehresmann connections generalize cartan connections 4. covariant derivative b rolling without slipping or twisting 1. rolling maps 2. the existence and uniqueness of rolling maps 3. relation to levi-civita and normal connections 4. transitivity of rolling without slipping or twisting c classification of one-dimensional effective klein pairs 1. classification of one-dimensional effective klein pairs d differential operators obtained from symmetry 1. real representations of so2(r) 2. operators on riemannian surfaces e characterization of principal bundles bibliography index |
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