From the conformal self-duality equations to the Manakov-Santini system
Exactly Solvable and Integrable Systems
2019-09-04 v1 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Abstract
Under two separate symmetry assumptions, we demonstrate explicitly how the equations governing a general anti-self-dual conformal structure in four dimensions can be reduced to the Manakov-Santini system, which determines the three-dimensional Einstein-Weyl structure on the space of orbits of symmetry. The two symmetries investigated are a non-null translation and a homothety, which are previously known to reduce the second heavenly equation to the Laplace's equation and the hyper-CR system, respectively. Reductions on the anti-self-dual null-K\"ahler condition are also explored in both cases.
Keywords
Cite
@article{arxiv.1902.07844,
title = {From the conformal self-duality equations to the Manakov-Santini system},
author = {Prim Plansangkate},
journal= {arXiv preprint arXiv:1902.07844},
year = {2019}
}