Superspace Geometry for Supermembrane Backgrounds

We construct part of the superspace vielbein and tensor gauge field in terms of the component fields of 11-dimensional on-shell supergravity. The result can be utilized to describe supermembranes and corresponding matrix models for Dirichlet particles in nontrivial supergravity backgrounds to second order in anticommuting coordinates. We exhibit the κ-invariance of the corresponding supermembrane action, which at this order holds for unrestricted supergravity backgrounds, the supersymmetry covariance and the resulting surface terms in the action.