2-DIMENSIONAL IDEAL MAGNETOHYDRODYNAMICS AND DIFFERENTIAL GEOMETRY

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