Einstein metrics, hypercomplex structures and the Toda field equation
微分几何
2009-09-25 v1 广义相对论与量子宇宙学
数学物理
math.MP
可精确求解与可积系统
solv-int
摘要
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.
引用
@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}
}
备注
9 pages