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

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.

Keywords:

• Camassa-Holm equation
• diffeomorphism group
• geodesic flow
• sectional curvature

AMS Subject Classifications:

• 35Q35
• 53C21
• 53D25
• 58B25
• 58D05

Notes

No potential conflict of interest was reported by the author.