Part ⅠRiemannian Holonomy Groups and Calibrated Geometry&Dominic Joyce 3
1 Introduction 3
2 Introduction to Holonomy Groups 4
3 Berger's Classification of Holonomy Groups 10
4 K？hler Geometry and Holonomy 14
5 The Calabi Conjecture 20
6 The Exceptional Holonomy Groups 26
7 Introduction to Calibrated Geometry 31
8 Calibrated Submanifolds in IRn 36
9 Constructions of SL m-folds in Cm 41
10 Compact Calibrated Submanifolds 50
11 Singularities of Special Lagrangian m-folds 57
12 The SYZ Conjecture, and SL Fibrations 63
Part ⅡCalabi-Yau Manifolds and Mirror Symmetry&Mark Gross 71
13 Introduction 71
14 The Classical Geometry of Calabi-Yau Manifolds 72
15 K？hler Moduli and Gromov-Witten Invariants 93
16 Variation and Degeneration of Hodge Structures 102
17 A Mirror Conjecture 121
18 Mirror Symmetry in Practice 122
19 The Strominger-Yau-Zaslow Approach to Mirror Symmetry 140
Part ⅢCompact Hyperk？hler Manifolds&Daniel Huybrechts 163
20 Introduction 163
21 Holomorphic Symplectic Manifolds 164
22 Deformations of Complex Structures 172
23 The Beauville-Bogomolov Form 177
24 Cohomology of Compact Hyperk？hler Manifolds 190
25 Twistor Space and Moduli Space 196
26 Projectivity of Hyperk？hler Manifolds 203
27 Birational Hyperk？hler Manifolds 213
28 The（Birational） K？hler Cone 221
References 227
Index 237