| 陈省身，开创并领导着整体微分几何、纤维丛微分几何、“陈省射示性类”等领域的研究，他是历史以来惟一获得世界数学界最高荣誉“沃尔夫奖”的会人，被称为“当今最伟大的数学家”，被国际数学界誉为“微分几何之父”。 |
| 1 Differentiable Manifolds . 1-1 Definition of Differentiable Manifolds 1-2 Tangent Spaces 1-3 Submanifolds 1-4 Frobenius‘ Theorem 2 Multilinear Algebra 2-1 Tensor Products 2-2 Tensors 2-3 Exterior Algebra 3 Exterior Differential Calculus 3-1 Tensor Bundles and Vector Bundles 3-2 Exterior Differentiation 3-3 Integrals of Differential Forms 3-4 Stokes‘ Formula 4 Connections 4-1 Connections on Vector Bundles 4-2 Affine Connections 4-3 Connections on Frame Bundles 5 Riemannian Geometry 5-1 The Fundamental Theorem of Riemannian Geometry 5-2 Geodesic Normal Coordinates 5-3 Sectional Curvature 5-4 The Gauss-Bonnet Theorem 6 Lie Group and Moving Frames 6-1 Lie Groups 6-2 Lie Transofrmation Groups 6-3 The Method of Moving Frames 6-4 Theory of Surfaces 7 Complex Manifolds 8 Finsler Geometry A Historical Notes B Differential Geometry and Theoretical Physics References Index |
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