Metrics of Special Holonomy and Gluing Theorems

by Alexei Kovalev

Metrics of Special Holonomy and Gluing Theorems Synopsis

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.

Book Information

ISBN: 9781860948435
Publication date: 1st July 2016
Author: Alexei Kovalev
Publisher: Imperial College Press
Format: Paperback
Pagination: 200 pages
Categories: Differential & Riemannian geometry,

About Alexei Kovalev

More About Alexei Kovalev

Share this book