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 (7)

• New Einstein-Sasaki Spaces in Five and Higher Dimensions
• Obstructions to the Existence of Sasaki-Einstein Metrics
• Cohomogeneity-one G2-structures
• Nearly hypo structures and compact Nearly Kähler 6-manifolds with conical singularities
• Unit Killing Vector Fields on Nearly Kahler Manifolds
• Classification des varietes approximativement kahleriennes homogenes
• Positively Curved Cohomogeneity One Manifolds and 3-Sasakian Geometry

Cited by in corpus (12)

• Counting BPS Operators in Gauge Theories: Quivers, Syzygies and Plethystics
• Obstructions to the Existence of Sasaki-Einstein Metrics
• New G2 holonomy cones and exotic nearly Kaehler structures on the 6-sphere and the product of a pair of 3-spheres
• Conical Kahler-Einstein metric revisited
• Spaces admitting homogeneous G2-structures
• Embedding into manifolds with torsion
• Einstein metrics and GIT stability
• On the homology of low dimensional cohomogeneity one manifolds
• Diffeomorphism type of 6-dimensional cohomogeneity one manifolds
• Polar manifolds and actions
• Ricci-flat metrics on the cone over ${\mathbb{CP}}^2\#\overline{{\mathbb{CP}}^2}$
• A class of Sasakian 5-manifolds