Invariant Ricci-flat metrics of cohomogeneity one with Wallach spaces as principal orbits

We construct a continuous 1-parameter family of smooth complete Ricci-flat metrics of cohomogeneity one on vector bundles over CP 2 , HP 2 and OP 2 with respective principal orbits G / K the Wallach spaces S U ( 3 ) / T 2 , Sp (3) / ( Sp (1) Sp (1) Sp (1)) and F 4 / Spin ( 8 ) . Almost all the Ricci-flat metrics constructed have generic holonomy. The only exception is the complete G 2 metric discovered in Bryant and Salamon (Duke Math J 58(3):829–850, 1989 ) and Gibbons et al. (Commun Math Phys 127(3):529–553, 1990 ). It lies in the interior of the 1-parameter family on ⋀ - 2 CP 2 . All the Ricci-flat metrics constructed have asymptotically conical limits given by the metric cone over a suitable multiple of the normal Einstein metric on G / K .