A Kähler metric is said to be Bochner-Kähler if its Bochner curvature vanishes. This is a nontrivial condition when the complex dimension of the underlying manifold is at least 2. In this article it will be shown that, in a certain well-defined sense, the space of Bochner-Kähler metrics in complex dimension n has real dimension n+1 and a recipe for an explicit formula for any Bochner-Kähler met...

We construct a new (singular) cohomogeneity-three metric of G 2 holonomy. The solution can be viewed as a triple intersection of smeared Taub-NUTs. The metric comprises three non-compact radial-type coordinate, with the principal orbits being a T 3 bundle over S 1. We consider an M-theory vacuum (Minkowski) 4 × M 7 where M 7 is the G 2 manifold. Upon reduction on a circle in the T 3 , we obtain...

In this paper, we look for metrics of cohomogeneity one in D = 8 and D = 7 dimensions with Spin(7) and G 2 holonomy respectively. In D = 8, we first consider the case of principal orbits that are S 7 , viewed as an S 3 bundle over S 4 with triaxial squashing of the S 3 fibres. This gives a more general system of first-order equations for Spin(7) holonomy than has been solved previously. Using n...