Metrics of Special Holonomy and Gluing Theorems
Seiten
2016
Imperial College Press (Verlag)
978-1-86094-842-8 (ISBN)
Imperial College Press (Verlag)
978-1-86094-842-8 (ISBN)
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Describes applications of the PDE methods to the construction and study of Ricci-flat metrics with special holonomy. This book pays attention to Ricci-flat Kahler (Calabi-Yau) structures on complex manifolds and hyper-Kahler structures on K3 surfaces.
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.
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.
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.
| Verlagsort | London |
|---|---|
| Sprache | englisch |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Geometrie / Topologie |
| ISBN-10 | 1-86094-842-1 / 1860948421 |
| ISBN-13 | 978-1-86094-842-8 / 9781860948428 |
| Zustand | Neuware |
| Informationen gemäß Produktsicherheitsverordnung (GPSR) | |
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