This book describes applications of the PDE methods to the construction and study of Ricci-flat metrics with special holonomy. Particular attention is paid to Ricci-flat Kahler (Calabi-Yau) structures on complex manifolds and hyper-Kahler structures on K3 surfaces. Complex manifolds are also an object of study in algebraic geometry and special consideration is given to the interplay between some well-known algebraic varieties (K3 surfaces, Fano threefolds, for example) and differential-geometric structures of special holonomy. The interplay between the gluing techniques, Calabi-Yau theory and algebraic geometry is further illuminated by the connected sum construction of compact 7-dimensional manifolds with holonomy G2.
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Produkt-Hinweis
Fadenheftung
Gewebe-Einband
ISBN-13
978-1-86094-842-8 (9781860948428)
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Schweitzer Klassifikation
Basic Material; Riemannian Manifolds with Asymptotically Cylindrical Ends; Complex Manifolds and the Calabi-Yau Geometry; K3 Surfaces; Complete Ricci-Flat Kahler Manifolds; The Kodaira-Spencer-Kuranishi Theory; Gluing Theorems for Manifolds with Cylindrical Ends; Compact Ricci-Flat Manifolds of Special Holonomy G2.