2010/10/31 by Martin Kohlmann
Physics and Astronomy · Mathematics · #math-ph #math.AP #math.MP
paper · pdf · doi:10.1088/1751-8113/44/22/225203
published as J. Phys. A: Math. Theor. 44 (2011) 225203 (17pp) · 19 pages
arxiv created 2011/05/04 · arxiv updated 2011/05/05
In this paper, we study two-component versions of the periodic Hunter-Saxton equation and its μ-variant. Considering both equations as a geodesic flow on the semidirect product of the circle diffeomorphism group \Diff(§) with a space of scalar functions on § we show that both equations are locally well-posed. The main result of the paper is that the sectional curvature associated with the 2HS is constant and positive and that 2μHS allows for a large subspace of positive sectional curvature. The issues of this paper are related to some of the results for 2CH and 2DP presented in [J. Escher, M. Kohlmann, and J. Lenells, J. Geom. Phys. 61 (2011), 436-452].