Killing vector fields in self-dual, Euclidean Einstein spaces with Λ≠0

Source abstract

Killing equations for self-dual, Euclidean Einstein spaces with nonvanishing cosmological term Λ are considered. It is shown that in this case one can reduce ten Killing equations to one master equation. Some important solutions of the master equation are found and one of these solutions is analyzed in detail as it leads to metrics defined by the field equation well known in Euclidean or complex relativity. Ernst potentials for the solutions considered are found.