A homogeneous Gibbons-Hawking ansatz and Blaschke products (Q1959671)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A homogeneous Gibbons-Hawking ansatz and Blaschke products |
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A homogeneous Gibbons-Hawking ansatz and Blaschke products (English)
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7 October 2010
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A natural notion of completeness for a Riemannian metric with a homothety (slice-completeness) is defined. A homogeneous Gibbons-Hawking ansatz is described. This ansatz forms the basis for the construction leading to non-flat slice-complete hyper-Kähler structures. Explicit formulae for various metrics that arise in this constructions are given. The obtained construction also gives rise to incomplete metrics on 3-dimensional contact manifolds that induce complete Carnot-Carathéodory distances.
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Riemannian metric
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hyper-Kähler metric
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hyper-Kähler structure
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Gibbons-Hawking potential
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Carnot-Carathéodory distance
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