Mathematics – Differential Geometry
Scientific paper
2006-06-14
Commun.Math.Phys.274:751-774,2007
Mathematics
Differential Geometry
22 pages. v2: remarks added concerning the parameter m having no effect on the metric, and the non-existence of metrics on the
Scientific paper
10.1007/s00220-007-0286-3
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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