Local heterotic geometry and self-dual Einstein-Weyl spaces

We consider the local heterotic geometry of Delduc and Valent which arises in (4, 0)-supersymmetry, and the self-dual Einstein-Weyl spaces of Pedersen and Swann. Both of these are hypercomplex and, by a consideration of spinors, we are able to find the relationship between them: roughly speaking, they have connections which agree on anti-self-dual bivectors but are opposite on self-dual bivectors. Some examples, including all compact ones, are discussed. © 1996 IOP Publishing Ltd.