EINSTEIN-METRICS ON S3-BUNDLE, R3-BUNDLE AND R4-BUNDLE

Starting from a 4 n-dimensional quaternionic Kähler base space, we construct metrics of cohomogeneity one in (4 n+3) dimensions whose level surfaces are the S2 bundle space of almost complex structures on the base manifold. We derive the conditions on the metric functions that follow from imposing the Einstein equation, and obtain solutions both for compact and non-compact (4 n+3)-dimensional spaces. Included in the non-compact solutions are two Ricci-flat 7-dimensional metrics with G2 holonomy. We also discuss two other Ricci-flat solutions, one on the R4 bundle over S3 and the other on an R4 bundle over S4. These have G2 and Spin(7) holonomy respectively. © 1990 Springer-Verlag.