Sasakian Geometry, Hypersurface Singularities, and Einstein Metrics

Abstract

We review our study of Sasakian geometry as an agent for proving the existence of Einstein metrics on odd dimensional manifolds. Particular emphasis is given to the Sasakian structures occuring on links of isolated hypersurface singularities.

This is an expository article that grew out of notes for the three lectures the second author presented during the XXIV-th Winter School of {\it Geometry and Physics} in Srni, Czech Republic, in January of 2004., 30 pages. Some new examples and references were added

References in corpus (3)

• On Eta-Einstein Sasakian Geometry
• Sasaki-Einstein Metrics on S^2 x S^3
• A New Infinite Class of Sasaki-Einstein Manifolds

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• A geometric dual of $c$-extremization
• Baryonic symmetries and M5 branes in the AdS_4/CFT_3 correspondence
• Localisation on Sasaki-Einstein manifolds from holomophic functions on the cone
• Supersymmetric AdS Backgrounds in String and M-theory
• A New Construction of Einstein-Sasaki Metrics in D >= 7
• On Sasaki-Einstein manifolds in dimension five
• Regularity of asymptotically conical Ricci-flat Kähler metrics
• Monge-Ampère operators, energy functionals, and uniqueness of Sasaki-extremal metrics
• Deformation of Sasakian metrics
• Seven-dimensional Einstein Manifolds from Tod-Hitchin Geometry
• Deformations and D-branes
• The AdS/CFT Correspondence and Symmetry Breaking