Geometry of a group of area-preserving diffeomorphisms

SDiffM, the group of area-preserving reparametrizations of two-dimensional surfaces M, plays an important role in the theory of relativistic membranes. We calculate the riemannian curvature of this group and analyze the stability of their geodesics. Since the geodesics are motions of an ideal fluid, this gives information on the instability of ideal fluid flow on M. (orig.)