Compact Manifolds With Special Holonomy (Oxford Mathematical Monographs)

Rating:
Summary: WELL DONE!
Review: This book is, as the author mentioned in the preface, a marriage of two parts. The first part provided more or less a self-contained introduction to the theory of Riemannian holonomy groups, which usually couldn't be found in differential geometry textbooks. The second part is a research monograph on exceptional holonomy groups, which is the subject that the author is famous at. This book contains lots of topics which are hard to be found in any other books. For example, it contains a proof of the Calabi conjecture, which I've never seen in anywhere else except Yau's original papers. It also has a concise introduction to Calabi-Yau manifolds, which includes lots of topics about CY manifolds that are hard to be found in just a single book. Overall, it's a great introduction to the theory of holonomy groups. And also provides a good start about differential geometric side of the theory of Calabi-Yau manifolds, together with a roughly complete list of further references.