Anti-self-dual Conformal Structures with Null Killing Vectors from Projective Structures

Einstein–Weyl structures from hyper–Kähl

Einstein–Weyl structures from hyper–Kähler metrics with conformal Killing vectors

✍ Maciej Dunajski; Paul Tod 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 120 KB

We consider four (real or complex) dimensional hyper-Kähler metrics with a conformal symmetry K . The three-dimensional space of orbits of K is shown to have an Einstein-Weyl structure which admits a shear-free geodesics congruence for which the twist is a constant multiple of the divergence. In thi