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Compact Manifolds with Special Holonomy (Oxford Mathematical Monographs),Used
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The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Khler geometry. Then the Calabi conjecture is proved and used to deduce the existence of compact manifolds with holonomy SU(m) (CalabiYau manifolds) and Sp(m) (hyperkhler manifolds). These are constructed and studied using complex algebraic geometry. The second half of the book is devoted to constructions of compact 7 and 8manifolds 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 19935. This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.
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