《卡拉比-丘流形和相关几何》是由2001年夏天norway，nordfjordeid讲述辛几何的讲义扩展而成。突出讲述calabi-yau是本书的最大特点。第一部分讲述完整群和已校准子流形，强调特殊拉格朗日算符子流形和syz猜想；第二部分运用代数几何讲述calabi-yau流形和镜子对称。最后一部分讲述紧hyperkahler流形，它具有的几何结果和calabi-yau流形有很大的关系。各部分之间过渡自然，衔接紧密紧密，是一部很好的教程。目次：黎曼完整群和已校准的几何；calabi-yau流形和镜子对称；紧hyperk?hler流形。本书由格罗斯等著。

Preface

Part 1 Riemannian Holonomy Groups and Calibrated Geometry

1 Introduction

2 Introduction to Holonomy Groups

3 Berger's Classification of Holonomy Groups

4 Kahler Geometry and Holonomy

5 The Calabi Conjecture

6 The Exceptional Holonomy Groups

7 Introduction to Calibrated Geometry

8 Calibrated Submanifolds in Rn

9 Constructions of SL m-folds in Cm

10 Compact Calibrated Submanifolds

11 Singularities of Special Lagrangian m-folds

12 The SYZ Conjecture, and SL Fibrations

Part 2 Calabi-Yau Manifolds and Mirror Symmetry

13 Introduction

14 The Classical Geometry of Calabi-Yau Manifolds

15 Kahler Moduli and Gromov-Witten Invariants

16 Variation and Degeneration of Hodge Structures

17 A Mirror Conjecture

18 Mirror Symmetry in Practice

19 The Strominger-Yau-Zaslow Approach to Mirror Symmetry

Part 3 Compact Hyperkahler Manifolds

20 Introduction

21 Holomorphic Symplectlc Manifolds

22 Deformations of Complex Structures

23 The Beauville-Bogomolov Form

24 Cohomology of Compact Hyperkahler Manifolds

25 Twistor Space and Moduli Space

26 Projectivity of Hyperkahler Manifolds

27 Birational Hyperkahler Manifolds

28 The （Birational） Kahler Cone

References

Index