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Compact Manifolds with Special Holonomy HIS036000 and detectThe 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) (Calabi Yau 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 8 manifolds with
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