1 Table of Contents: “... for harmonic maps and rigidity theorems -- 5.1 The Bochner formula for harmonic one-forms and harmonic maps...”

2 Table of Contents: “... theorem -- 4 Mañé’s Formula for Geodesic Flows and Convex Billiards -- 4.1 Time shifts that avoid...”

3 Table of Contents: “....3 Taylor’s Theorem -- 2 Differential Forms -- 2.1 Line Integrals -- 2.2 One Forms -- 2.3 Wedge Product -- 2.4...”

4 Table of Contents: “...I. Introduction -- 1.1 Vector Bundles -- 1.2 Harmonic Maps -- 1.3 A Bochner Type Formula -- 1...”

5 Table of Contents: “... cohomology III: Morse case by multisection -- 21.Tree-like K-system: A1 structure I: statement -- 22.Tree...”

6 Table of Contents: “... Extremal Kähler metrics -- 2.1 The space of Kähler metrics -- 2.2 A brief review of Chern classes -- 2.3...”

7 Table of Contents: “...) and (1,2) -- 3.3. Generalized spheres with tubes -- 3.4. The sewing formulas and the convergence...”

8 Table of Contents: “...1. Equivalence Relations -- 2 Mappings -- 3 The Real Numbers -- 4 Axiom Systems -- One Absolute...”

9 Table of Contents: “...1. The Matrix Exponential; Some Matrix Lie Groups -- 2. Adjoint Representations and the Derivative...”

10 Table of Contents: “...Abhyankar’s Recursive Formula Regarding Standard Bi-Tableau -- 16 Correspondences Between Tableaux...”

11 Table of Contents: “... And Global Flow -- 1.6 Cultural Digression -- 2. Differentiable Manifolds -- 2.1 Submanifolds of Rn -- 2.2...”

12 Table of Contents: “...1 L.c.K. Manifolds -- 2 Principally Important Properties -- 2.1 Vaisman’s conjectures -- 2.2...”

13 Table of Contents: “... tower -- 4.1. Introduction -- 4.2. Commuting squares -- 4.3. Wenzl’s index formula -- 4.4. Examples...”

14 Table of Contents: “....11 Appendix: The Planimeter -- 2 Spherical Geometry -- 2.1 Geodesics -- 2.2 Geodesics on Spheres -- 2.3...”

15 Table of Contents: “... bivector -- 1.2 The Schouten-Nijenhuis bracket -- 1.3 Coordinate expressions -- 1.4 The Koszul formula...”

16 Table of Contents: “... Theorems -- 4.8 Integrals Over a Set -- 4.9 Fubini’s Theorem -- 5 Integrals on Manifolds -- 5.1...”

17 Table of Contents: “... Sheaves -- 2. The Existence of Sections of Sheaves -- § 2.1 The Sections of Invertible Sheaves (Part I...”

18 Table of Contents: “... -- 2 The one-dimensional case: elliptic curves -- 2.1 General Features of Elliptic Curves -- 2.2...”

19 Table of Contents: “... neighbourhoods -- § 2. Local mapping degree -- 2.1. Local decomposition revisited -- 2.2. Local mapping degree...”

20 Table of Contents: “...2 Floer theory in action.-2.1 A brief sketch of Floer theory .-2.2 Width and torsion.-2.3 A...”