Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation

Martin Bauer; Martins Bruveris; Peter W. Michor; Philipp Harms

arxiv: 1102.0236 · v3 · pith:2JHMLU6Enew · submitted 2011-02-01 · 🧮 math.AP · math.DG

Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation

Martin Bauer , Martins Bruveris , Philipp Harms , Peter W. Michor This is my paper

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keywords geodesicmetricdistanceequationkdv-equationriemannianvanishingendowed

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The Virasoro-Bott group endowed with the right-invariant $L^2$-metric (which is a weak Riemannian metric) has the KdV-equation as geodesic equation. We prove that this metric space has vanishing geodesic distance.

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Vanishing geodesic distance for the Riemannian metric with geodesic equation the KdV-equation

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