Toric G_2 and Spin(7) holonomy spaces from gravitational instantons and other examples

Non-compact G_2 holonomy metrics that arise from a T^2 bundle over a hyper-Kahler space are discussed. These are one parameter deformations of the metrics studied by Gibbons, Lu, Pope and Stelle in hep-th/0108191. The G_2 extensions of the Taub-Nut and the Eguchi-Hanson gravitational instantons as well as other examples are found explicitly. By using the Apostolov-Salamon theorem math.DG/0303197, we construct a new example that, still being a T^2 bundle over hyper-Kahler, represents a non trivial deformation of the metrics studied in hep-th/0108191. We then review the Spin(7) metrics arising from a T^3 bundle over a hyper-Kahler and we find a two parameter deformation of such spaces. We also present new examples. The relation between these spaces to the half-flat structures and almost G_2 holonomy spaces is briefly discussed