On some Euclidean Einstein metrics (Q1820456)

The authors study the complex manifold associated with a nonlinear superposition of the Eguchi-Hanson and the pseudo-Fubini-Study metrics. The apparent singularities of the metric can be resolved only if the Eguchi-Hanson parameter satisfies a certain condition with \(n\geq 3\). The authors give a geometrical explanation of this fact. A generalization of the Gegenberg-Das metric is given to obtain a triaxial vacuum solution.