微分几何

cartan geometries1. the base definition of cartan geometries2. the principal bundle hidden in a cartan geometry3. the bundle definition of a cartan geometry4. development, geometric orientation, and holonomy5. flat cartan geometries and uniformization6. cartan space forms7. symmetric spaces6 riemannian geometry1. the model euclidean space2. euclidean and riemannian geometry3. the equivalence problem for riemannian metrics4. riemannian space forms5. subgeometry of a riemannian geometry6. isoparametric submanifolds7 msbius geometry1. the msbius and weyl models2. msbius and weyl geometries3. equivalence problems for a conformal metric4. submanifolds of msbius geometry5. immersed curves6. immersed surfaces8 projective geometry1. the projective model2. projective cartan geometries3. the geometry of geodesics4. the projective connection in a riemannian geometry5. a brief tour of projective geometrya ehresmann connections1. the geometric origin of ehresmann connections2. the reductive case3. ehresmann connections generalize cartan connections4. covariant derivativeb rolling without slipping or twisting1. rolling maps2. the existence and uniqueness of rolling maps3. relation to levi-civita and normal connections4. transitivity of rolling without slipping or twistingc classification of one-dimensional effective klein pairs1. classification of one-dimensional effective klein pairsd differential operators obtained from symmetry1. real representations of so2(r)2. operators on riemannian surfacese characterization of principal bundlesbibliographyindex

《微分几何(英文影印版)》系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。内容体系脉络清晰，完整。前四章全面讲述了微分拓扑、叶状结构，李群和齐次空间；第五章讲述了产生齐次空间的cartan几何，和黎曼几何产生欧几里得几何很相似。cartan几何的一个很漂亮的方面将曲率看作是破缺对称性的精确局部度量；最后三章研究了黎曼几何、共形几何和射影几何；五个附录中介绍了cartan和ehresmann联络和从对称的角度考虑散度和旋度算子的不同特性。目次：微分拓扑；叶状结构；微积分基本定理；klein几何；cartan几何；黎曼几何；mobius几何；射影几何。附录：ehresmann联络；不滑动和扭曲的滚动；一维有效klein对的分类；来自对称的微分算子；主丛的分类。　　读者对象：数学专业的高年级本科生、研究生和科研人员。