Supermembranes in curved superspace and near-horizon geometries

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We give a description of supermembranes in nontrivial target-space geometries. A special class are the $AdS_4\times S^7$ and $AdS_7\times S^4$ spaces that have the maximal number of 32 supersymmetries.
Lecture presented at the 22-nd Johns Hopkins Workshop, Novelties in String Theory, Göteborg, August 20-22, 1998. LateX 18 pp

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