Riemannian Holonomy Groups and Calibrated Geometry

• Accessible to graduate students in both Mathematics and Physics
• Surveys current research and states open problems, particularly in calibrated geometry
• Thorough coverage, major proofs such as the Calabi conjecture are provided in full
• Extensive, up-to-date bibliography

Readership: Graduates and researchers in Mathematics and Physics

Dominic D. Joyce, University of Oxford

"This graduate level text covers an exciting and active area of research at the crossroads of several different fields in mathematics and physics." - L'enseignement Mathematique

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