On Ricci solitons and twistorial harmonic morphisms
Differential Geometry
2012-10-18 v1
Abstract
We study the soliton flow on the domain of a twistorial harmonic morphism between Riemannian manifolds of dimensions four and three. Assuming real-analyticity, we prove that, for the Gibbons-Hawking construction, any soliton flow is uniquely determined by its restriction to any local section of the corresponding harmonic morphism. For the Beltrami fields construction, we identify a contour integral whose vanishing characterises the trivial soliton flows.
Keywords
Cite
@article{arxiv.1210.4688,
title = {On Ricci solitons and twistorial harmonic morphisms},
author = {Paul Baird and Radu Pantilie},
journal= {arXiv preprint arXiv:1210.4688},
year = {2012}
}
Comments
13 pages