Compact Manifolds with Special Holonomy (Oxford Mathematical Monographs) (Hardcover)

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Description


The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and K hler 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) (hyperk hler 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 This is the first book to be written about them, and contains much previously unpublished material which significantly improves the original constructions.


Product Details
ISBN: 9780198506010
ISBN-10: 0198506015
Publisher: Oxford University Press, USA
Publication Date: September 21st, 2000
Pages: 448
Language: English
Series: Oxford Mathematical Monographs