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Metrics of Special Holonomy and Gluing Theorems by Alexei Kovalev

Metrics of Special Holonomy and Gluing Theorems


Metrics of Special Holonomy and Gluing Theorems by Alexei Kovalev

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.

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Book Info

Publication date

1st July 2016


Alexei Kovalev

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Imperial College Press


200 pages


Differential & Riemannian geometry



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