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.
Conti, D. (2007). Cohomogeneity one Einstein-Sasaki 5-manifolds. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 274(3), 751-774 [10.1007/s00220-007-0286-3].
Cohomogeneity one Einstein-Sasaki 5-manifolds
CONTI, DIEGO
2007
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.
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