Local constraints on 3-dimensional Einstein-Weyl spaces: A spinorial treatment (Q2775852)

Following the work of \textit{M. G. Eastwood} and \textit{K. P. Tod} [J. Reine Angew. Math. 491, 183-198 (1997; Zbl 0876.53029)], the author considers the question of devising a spinor calculus on 3-dimensional Einstein-Weyl spaces in which the Einstein-Weyl equations can be expressed as a closed system involving certain spinor fields associated with the underlying Einstein-Weyl structure. The principal result is a proof that there does not exist, even locally, any 3-dimensional conformal 3-manifold admitting an Einstein-Weyl structure. Contents include: an introduction (which contains an overview of Einstein-Weyl spaces and the spinor calculus); the main results (including three theorems); and an appendix (which includes -- without proof -- six spinor identities which are needed in the proofs of the theorems).