Abstract
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.
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