2-DIMENSIONAL IDEAL MAGNETOHYDRODYNAMICS AND DIFFERENTIAL GEOMETRY

It is shown that equations of two-dimensional ideal magnetohydrodynamics may be regarded as geodesic equations on appropriate infinite dimensional Lie group. The physical interpretation of such a geometric picture is given using an analogy with two-and-a-half-dimensional ideal hydrodynamics. The sectional curvature responsible for the separation of neighbouring geodesics and, hence, for stability is calculated.