Eguchi-Hanson metrics with cosmological constant

The author constructs a solution to Einstein's equations with a cosmological constant. The metric contains two parameters (a,b). When b=0 the metric is recognized as the Eguchi-Hanson I (II) solution with anti-self-dual Weyl tensor W^-. When a=0 it is seen to be the (pseudo) Fubini Study metric with a self-dual Weyl tensor W⁺. The solution has a Weyl tensor W⁺+W^-, is a Kahler metric, and is of Petrov type D. The author shows that in some cases the metric is complete.