Cohomogeneity one Einstein-Sasaki 5-manifolds

Abstract

We consider hypersurfaces in Einstein-Sasaki 5-manifolds which are tangent to the characteristic vector field. We introduce evolution equations that can be used to reconstruct the 5-dimensional metric from such a hypersurface, analogous to the (nearly) hypo and half-flat evolution equations in higher dimensions. We use these equations to classify Einstein-Sasaki 5-manifolds of cohomogeneity one.

22 pages. v2: remarks added concerning the parameter m having no effect on the metric, and the non-existence of metrics on the link L(2,2,2,3); statements and proofs of main theorems modified in light of a more precise characterization of the cohomogeneity one diagrams. v3: presentation improved. To appear in Comm. Math. Phys

References in corpus (2)

• Obstructions to the Existence of Sasaki-Einstein Metrics
• Classification des varietes approximativement kahleriennes homogenes

Cited by in corpus (8)

• Obstructions to the Existence of Sasaki-Einstein Metrics
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• Einstein metrics and GIT stability
• On the homology of low dimensional cohomogeneity one manifolds
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• Polar manifolds and actions
• Ricci-flat metrics on the cone over ${\mathbb{CP}}^2\#\overline{{\mathbb{CP}}^2}$
• A class of Sasakian 5-manifolds