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Sasakian geometry

Sasakian geometry
Catalogue Information
Field name Details
Dewey Class 516.373 (DDC 23)
Title Sasakian geometry (EB) / Charles P. Boyer and Krzysztof Galicki.
Author Boyer, Charles P.
Added Personal Name Galicki, Krzysztof
Other name(s) Oxford Scholarship Online
Publication Oxford, UK : Oxford University Press , 2008
Physical Details 1 online resource
Series Oxford mathematical monographs
ISBN 9780191713712
Note Print publication date: 2007. - Published to Oxford Scholarship Online: January 2008
Summary Note Sasakian manifolds were first introduced in 1962. This book's main focus is on the intricate relationship between Sasakian and Kähler geometries, especially when the Kähler structure is that of an algebraic variety. The book is divided into three parts. The first five chapters carefully prepare the stage for the proper introduction of the subject. After a brief discussion of G-structures, the reader is introduced to the theory of Riemannian foliations. A concise review of complex and Kähler geometry precedes a fairly detailed treatment of compact complex Kähler orbifolds. A discussion of the existence and obstruction theory of Kähler-Einstein metrics (Monge-Ampère problem) on complex compact orbifolds follows. The second part gives a careful discussion of contact structures in the Riemannian setting. Compact quasi-regular Sasakian manifolds emerge here as algebraic objects: they are orbifold circle bundles over compact projective algebraic orbifolds. After a discussion of symmetries of Sasakian manifolds in Chapter 8, the book looks at Sasakian structures on links of isolated hypersurface singularities in Chapter 9. What follows is a study of compact Sasakian manifolds in dimensions three and five focusing on the important notion of positivity. The latter is crucial in understanding the existence of Sasaki-Einstein and 3-Sasakian metrics, which are studied in Chapters 11 and 13. Chapter 12 gives a fairly brief description of quaternionic geometry which is a prerequisite for Chapter 13. The study of Sasaki-Einstein geometry was the original motivation for the book. The final chapter on Killing spinors discusses the properties of Sasaki-Einstein manifolds, which allow them to play an important role as certain models in the supersymmetric field theories of theoretical physics.:
Mode of acces to digital resource Digital book.- Oxford : Oxford University Press, 2008. - Mode of access: World Wide Web. System requirements: Internet Explorer 6.0 (or higher) or Firefox 2.0 (or higher)
System details note Online access is restricted to subscribing institutions through IP address (only for SISSA internal users)
Internet Site http://dx.doi.org/10.1093/acprof:oso/9780198564959.001.0001
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