On Sasaki-Einstein manifolds in dimension five

Abstract

We prove the existence of Sasaki-Einstein metrics on certain simply connected 5-manifolds where until now existence was unknown. All of these manifolds have non-trivial torsion classes. On several of these we show that there are a countable infinity of deformation classes of Sasaki-Einstein structures.

18 pages, Exposition was expanded and a reference added

References in corpus (3)

• Obstructions to the Existence of Sasaki-Einstein Metrics
• Semi-continuity of complex singularity exponents and Kähler-Einstein metrics on Fano orbifolds
• Sasakian Geometry, Hypersurface Singularities, and Einstein Metrics

Cited by in corpus (7)

• Sasaki-Einstein metrics and K-stability
• Killing-Yano tensors and some applications
• Singularity, Sasaki-Einstein manifold, Log del Pezzo surface and $\mathcal{N}=1$ AdS/CFT correspondence: Part I
• Simply connected Sasaki-Einstein rational homology 5-spheres
• The local moduli of Sasaki-Einstein rational homology 7-spheres and invertible polynomials
• Negative Sasakian structures on simply-connected 5-manifolds
• Some topics in Sasakian geometry, a survey