Riemannian Holonomy Groups and Calibrated Geometry (Oxford Graduate Texts in Mathematics)

Joyce, Dominic D.

Oxford University Press（2007/02発売）

• 製本 Hardcover:ハードカバー版／ページ数 320 p.
• 言語 ENG
• 商品コード 9780199215607
• DDC分類 516.373

基本説明

Thorough coverage, major proofs such as the Calabi conjecture are provided in full.

Full Description

This graduate level text covers an exciting and active area of research at the crossroads of several different fields in Mathematics and Physics. In Mathematics it involves Differential Geometry, Complex Algebraic Geometry, Symplectic Geometry, and in Physics String Theory and Mirror Symmetry. Drawing extensively on the author's previous work, the text explains the advanced mathematics involved simply and clearly to both mathematicians and physicists. Starting with the basic geometry of connections, curvature, complex and Kähler structures suitable for beginning graduate students, the text covers seminal results such as Yau's proof of the Calabi Conjecture, and takes the reader all the way to the frontiers of current research in calibrated geometry, giving many open problems.

Contents

Preface ; 1. Background material ; 2. Introduction to connections, curvature and holonomy groups ; 3. Riemannian holonomy groups ; 4. Calibrated geometry ; 5. Kahler manifolds ; 6. The Calabi Conjecture ; 7. Calabi-Yau manifolds ; 8. Special Lagrangian geometry ; 9. Mirror Symmetry and the SYZ Conjecture ; 10. Hyperkahler and quaternionic Kahler manifolds ; 11. The exceptional holonomy groups ; 12. Associative, coassociative and Cayley submanifolds ; References ; Index