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New Results in Sasaki—Einstein Geometry

  • James Sparks
Part of the Progress in Mathematics book series (PM, volume 271)

Abstract

This article is a summary of some of the author’s work on Sasaki–Einstein geometry. A rather general conjecture in string theory known as the AdS/CFT correspondence relates Sasaki–Einstein geometry, in low dimensions, to superconformal field theory; properties of the latter are therefore reflected in the former, and vice versa. Despite this physical motivation, many recent results are of independent geometrical interest and are described here in purely mathematical terms: explicit constructions of infinite families of both quasi-regular and irregular Sasaki–Einstein metrics; toric Sasakian geometry; an extremal problem that determines the Reeb vector field for, and hence also the volume of, a Sasaki–Einstein manifold; and finally, obstructions to the existence of Sasaki–Einstein metrics. Some of these results also provide new insights into Kähler geometry, and in particular new obstructions to the existence of Kähler–Einstein metrics on Fano orbifolds.

Keywords

Toric Variety Ahler Manifold Einstein Metrics Einstein Manifold Reeb Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Boston, a part of Springer Science+Business Media LLC 2009

Authors and Affiliations

  • James Sparks
    • 1
    • 2
  1. 1.Department of MathematicsHarvard UniversityCambridgeUSA
  2. 2.Jefferson Physical LaboratoryHarvard UniversityCambridgeUSA

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