Einstein metrics, hypercomplex structures and the Toda field equation
Differential Geometry
2009-09-25 v1 General Relativity and Quantum Cosmology
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
solv-int
Abstract
We obtain explicitly all solutions of the SU(infinity) Toda field equation with the property that the associated Einstein-Weyl space admits a 2-sphere of divergence-free shear-free geodesic congruences. The solutions depend on an arbitrary holomorphic function and give rise to new hyperKahler and selfdual Einstein metrics with one dimensional isometry group. These metrics each admit a compatible hypercomplex structure with respect to which the symmetries are triholomorphic.
Cite
@article{arxiv.math/9911121,
title = {Einstein metrics, hypercomplex structures and the Toda field equation},
author = {David M. J. Calderbank and Paul Tod},
journal= {arXiv preprint arXiv:math/9911121},
year = {2009}
}
Comments
9 pages