On Ricci-flat twistor theory (Q1840692)

The author of this interesting paper is the creator of the twistor theory. He defines the main purpose of the paper in the following way: ``The problem of introducing self-dual Weyl curvature into the geometry of twistor space has been referred to as the (gravitational) googly problem of twistor theory\dots{} Somewhat over a year ago, a new approach to the relevant googly geometry has come about (Penrose, 1999)\dots{} The purpose of this article is to point out that there is also a Riemannian version of the new googly geometry, although I have not worked out all the requirements for this. It is my hope that these ideas will be taken up seriously by someone and that there may be some interesting new things to say about general (neither self-dual nor anti-self-dual) Ricci-flat Riemannian \(4\)-spaces in accordance with these twistorial ideas. I can give only a very brief account on the new googly geometry here\dots{}''.