Metrics of Special Holonomy and Gluing Theorems

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.

Product details

• Authors: Alexei Kovalev, Kovalev Alexei
• Publisher: Ingram Publishers Services
• Languages: English
• Product format: Hardback
• Released: 01.07.2016
• EAN: 9781860948428
• ISBN: 978-1-86094-842-8
• No. of pages: 200
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Geometry; MATHEMATICS / Geometry / Differential, Differential & Riemannian geometry, Differential and Riemannian geometry