Riemannian Holonomy Groups and Calibrated Geometry
Series: Oxford Graduate Texts in Mathematics; 12;
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Product details:
- Publisher OUP Oxford
- Date of Publication 22 February 2007
- ISBN 9780199215591
- Binding Paperback
- No. of pages320 pages
- Size 232x157x17 mm
- Weight 461 g
- Language English 0
Categories
Short description:
Riemannian holonomy groups and calibrated geometry covers an exciting and active area of research at the crossroads of several different fields in Mathematics and Physics. Drawing on the author's previous work the text has been written to explain the advanced mathematics involved simply and clearly to graduate students in both disciplines.
MoreLong 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.
MoreTable of Contents:
Preface
Background material
Introduction to connections, curvature and holonomy groups
Riemannian holonomy groups
Calibrated geometry
Kähler manifolds
The Calabi Conjecture
Calabi-Yau manifolds
Special Lagrangian geometry
Mirror Symmetry and the SYZ Conjecture
Hyperkähler and quaternionic Kähler manifolds
The exceptional holonomy groups
Associative, coassociative and Cayley submanifolds
References
Index
