Abstract
The geometric structure equations of a manifold satisfying the vacuum Einstein equations are expressed in terms of a complexification of the space of 2-forms adapted to the Petrov classification. The Petrov type III problem is invariantly reduced to the solution of one partial differential equation. Examples of solutions containing one arbitrary function are given, corresponding to spaces with groups of motions of dimensions 0, 1, and 2.

This publication has 0 references indexed in Scilit: