G3-homogeneous gravitational instantons

Understand

We provide an exhaustive classification of self-dual four-dimensional gravitational instantons foliated with three-dimensional homogeneous spaces, i.e.

• homogeneous self-dual metrics on four-dimensional Euclidean spaces admitting a Bianchi simply transitive isometry group.
• The classification pattern is based on the algebra homomorphisms relating the Bianchi group and the duality group SO(3).
• New and general solutions are found for Bianchi III.