Abstract: We investigate L²-metrics on shape space weighted by expressions in volume and mean curvature. Here, shape space is the manifold of unparametrized, compact, oriented, immersed hypersurfaces in n-space. The geodesic equation and sectional curvature are calculated, and sufficient conditions for non-vanishing geodesic distance are stated. Thereby we will use the variational formulas presented in our talk on November, 16.