The book starts with a thorough introduction to connections and holomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existence of compact manifolds with holomy 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 holomy groups 92 and Spin(7). Many new examples are given, and their Betti numbers calculated. The first kwn 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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.
University lecturer and tutorial fellow at Lincoln College, Oxford Dr D Joyce Lincoln College Oxford OX1 3DR Tel. 01865 279800 Email: email@example.com