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Riemannian Holonomy Groups and Calibrated Geometry

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Riemannian Holonomy Groups and Calibrated Geometry Cover

 

Synopses & Reviews

Publisher Comments:

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.

About the Author

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 and Spin(7), and special Lagrangian submanifolds, a kind of calibrated submanifold. He is married, with two daughters.

Table of Contents

Preface

1. Background material

2. Introduction to connections, curvature and holonomy groups

3. Riemannian holonomy groups

4. Calibrated geometry

5. Kñhler manifolds

6. The Calabi Conjecture

7. Calabi-Yau manifolds

8. Special Lagrangian geometry

9. Mirror Symmetry and the SYZ Conjecture

10. Hyperkñhler and quaternionic Kñhler manifolds

11. The exceptional holonomy groups

12. Associative, coassociative and Cayley submanifolds

References

Index

Product Details

ISBN:
9780199215607
Author:
Joyce, Dominic D.
Publisher:
Oxford University Press, USA
Subject:
Topology
Subject:
Mathematics | Pure Mathematics
Subject:
Geometry, riemannian
Subject:
Holonomy groups.
Subject:
Topology - General
Subject:
Geometry, analytic
Subject:
Geometry - Non-Euclidean
Subject:
MATHEMATICS / Topology
Series:
Oxford Graduate Texts in Mathematics
Series Volume:
12
Publication Date:
20070531
Binding:
HARDCOVER
Grade Level:
Professional and scholarly
Language:
English
Illustrations:
Y
Pages:
314
Dimensions:
6 x 9.3 x 0.9 in 1.325 lb

Related Subjects

History and Social Science » World History » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Geometry » General
Science and Mathematics » Mathematics » Topology

Riemannian Holonomy Groups and Calibrated Geometry New Hardcover
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