Riemannian geometry and geometric Analysis      jurgen Jost 著作等身

第一章 Remannian Manifolds      1.6 heat flow method

第二章 Lie groups and Vector Bundles   [Bundle chart of TS^1]

2.1 Vector Bundles   2.2 Complex and Holomorphic Vector Bundles :   2.3 Integral Curves of Vector Fields : Lie Algebra

2.4 Symplectic Structures   2.5 Lie Groups   2.6 Spin Strutures

第三章 The Laplace operator and Harmonic Differential Forms
3.1 The Laplace Operator on functions   3.2 The spetrum of the Laplace operator   3.3 The Laplace operator on forms

3.4 Representing Cohomology Classes by harmonic forms   3.5 The heat flow and harmonic forms

 [Rellich Embedding Theorem] [Laplacian的幾何意義]...量化了函數在該點附近的平均值與中心值得偏差

第四章 Connections and Curvature

第五章 Geometry of Submanifolds

第六章 Geodesic and Jacobi Fields

第七章 Symmetric Spaces and Kahler Manifolds

第八章 Morse Theory and Floer Homology

第九章 Hamonic Maps between Riemannian Manifolds

第十章 Harmonic Maps from Riemann Surfaces

第11章 Variational problems from Quntum Field Theory

微分幾何 辛幾何 代數幾何是不同的範疇   幾何分析(丘)