Riemannian Holonomy Groups and Calibrated Geometry by Dominic D. JoyceRiemannian Holonomy Groups and Calibrated Geometry by Dominic D. Joyce

Riemannian Holonomy Groups and Calibrated Geometry

byDominic D. Joyce

Hardcover | March 22, 2007

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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 MirrorSymmetry. 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 Kahler structures suitable for beginning graduatestudents, 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.
Dominic Joyce came up to Oxford University in 1986 to read Mathematics. He held an EPSRC Advanced Research Fellowship from 2001-2006, was recently promoted to professor, and now leads a research group in Homological Mirror Symmetry. His main research areas so far have been compact manifolds with the exceptional holonomy groups G_2 an...
Title:Riemannian Holonomy Groups and Calibrated GeometryFormat:HardcoverDimensions:320 pages, 9.21 × 6.14 × 0.87 inPublished:March 22, 2007Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:019921560X

ISBN - 13:9780199215607


Table of Contents

Preface1. Background material2. Introduction to connections, curvature and holonomy groups3. Riemannian holonomy groups4. Calibrated geometry5. Kahler manifolds6. The Calabi Conjecture7. Calabi-Yau manifolds8. Special Lagrangian geometry9. Mirror Symmetry and the SYZ Conjecture10. Hyperkahler and quaternionic Kahler manifolds11. The exceptional holonomy groups12. Associative, coassociative and Cayley submanifoldsReferencesIndex