For scalar and electromagnetic fields we evaluate the vacuum expectation value of the energy-momentum tensor induced by a curved boundary in the Robertson–Walker spacetime with negative spatial curvature. In order to generate the vacuum densities we use the conformal relation between the Robertson–Walker and Rindler spacetimes and the corresponding results for a plate moving by uniform proper acceleration through the Fulling–Rindler vacuum. For the general case of the scale factor the vacuum energy-momentum tensor is presented as the sum of the boundary free and boundary induced parts.