Curvature computations for a two-component Camassa-Holm equation with vorticity

Martin Kohlmann

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arXiv · 1509.00694

Curvature computations for a two-component Camassa-Holm equation with vorticity

Martin Kohlmann

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Abstract

In the present paper, a two-component Camassa-Holm (2CH) system with vorticity is studied as a geodesic flow on a suitable Lie group. The paper aims at presenting various details of the geometric formalism and a major result is the computation of the sectional curvature $K$ of the underlying configuration manifold. As a further result, we show that there are directions for which $K$ is strictly positive and bounded away from zero.

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Martin Kohlmann. 2015-09-02. Curvature computations for a two-component Camassa-Holm equation with vorticity. https://arxiv.org/abs/1509.00694

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