黑料网

I will present two results in connection with the anti-self-dual (ASD) conformal structures and Einstein-Weyl structures. Firstly, motivated by the fact that any 4-dimensional ASD structure with a non-null conformal Killing symmetry gives an Einstein-Weyl structure on the 3-dimensional space of orbits, I will show that the ASD conformal equation in neutral signature can be explicitly reduced, by a simple transformation, to the Manakov-Santini system which governs generic Lorentzian Einstein-Weyl structures. Secondly, a generalization of the dKP equation which determines a family of Einstein-Weyl structures in an arbitrary dimension will be discussed, and an extension of the quadric ansatz method presented as an attempt to find solutions of the equation.