A homogeneous Gibbons-Hawking ansatz and Blaschke products
Differential Geometry
2010-08-27 v1 Symplectic Geometry
Abstract
A homogeneous Gibbons-Hawking ansatz is described, leading to 4-dimensional hyperkahler metrics with homotheties. In combination with Blaschke products on the unit disc in the complex plane, this ansatz allows one to construct infinite-dimensional families of such hyperkahler metrics that are, in a suitable sense, complete. Our construction also gives rise to incomplete metrics on 3-dimensional contact manifolds that induce complete Carnot-Caratheodory distances.
Keywords
Cite
@article{arxiv.0807.0086,
title = {A homogeneous Gibbons-Hawking ansatz and Blaschke products},
author = {Hansjörg Geiges and Jesús Gonzalo},
journal= {arXiv preprint arXiv:0807.0086},
year = {2010}
}
Comments
16 pages, 5 figures