Curvature computations for a two-component Camassa-Holm equation with vorticity. Issue 2 (25th January 2017)

• Record Type: Journal Article
• Authors: Kohlmann, Martin
• Is Part Of: Applicable analysis. Volume 96:Issue 2(2017)
• Page Start: 307
• Page End: 323
• Publication Date: 2017-01-25
• Subjects: Camassa-Holm equation -- diffeomorphism group -- geodesic flow -- sectional curvature; 35Q35 -- 53C21 -- 53D25 -- 58B25 -- 58D05; Mathematical analysis -- Periodicals; 515
• DOI: 10.1080/00036811.2015.1134784
• Languages: English
• ISSNs: 0003-6811

Abstract

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.