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arXiv · 0807.0086

A homogeneous Gibbons-Hawking ansatz and Blaschke products

Hansjörg Geiges·Jesús Gonzalo
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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.

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Hansjörg Geiges, Jesús Gonzalo. 2008-07-01. A homogeneous Gibbons-Hawking ansatz and Blaschke products. https://arxiv.org/abs/0807.0086

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