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Zusatztext The first part is a very effective introduction to basic notions and results of modern differential geometry ... This book is highly recommended for people who are interested in the very recent developments of differential geometry and its relationships with present research in theoretical physics. Informationen zum Autor University lecturer and tutorial fellow at Lincoln College, Oxford Dr D Joyce Lincoln College Oxford OX1 3DR Tel. 01865 279800 Email: dominic.joyce@lincoln.ox.ac.uk Klappentext The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existence of compact manifolds with holonomy SU(m) (Calabi-Yau manifolds) and Sp(m) (hyperkahler manifolds). These are constructed and studied using complex algebraic geometry. The second half of the book is devoted to constructions of compact 7- and 8-manifolds with the exceptional holonomy groups 92 and Spin(7). Many new examples are given, and their Betti numbers calculated. The first known examples of these manifolds were discovered by the author in 1993-5. This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions. Zusammenfassung This is a combination of a graduate textbook on Riemannian holonomy groups, and a research monograph on compact manifolds with the exceptional holonomy groups G2 and Spin (7). It is the first book on compact manifolds with exceptional holonomy, and contains much new research material and many new examples.
