Einstein metrics, hypercomplex structures and the Toda field equation
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- November 1999
- DOI:
- arXiv:
- arXiv:math/9911121
- Bibcode:
- 1999math.....11121C
- Keywords:
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- Mathematics - Differential Geometry;
- General Relativity and Quantum Cosmology;
- Mathematical Physics;
- Nonlinear Sciences - Exactly Solvable and Integrable Systems;
- 53C25;
- 53A30 (Primary) 83C05;
- 53B38 (Secondary)
- E-Print:
- 9 pages