Some Gravitational Instantons

Abstract

All known gravitational instantons with $\Lambda > 0$ ($S^4, CP^2, S^2 \times S^2$ and $CP # \overline{CP}^2$) are described. They are all special cases of the Taub-NUT-$\Lambda$ local solution. Hence they are Type D and are locally conformably K\"ahler. They all may be expressed in Bianchi IX form and have four or more Killing vectors.