The usual supermembrane solution of D = 11 supergravity interpolates between R11 and AdS4 × round R7, has symmetry P3 × SO(8) and preserves 1 2 of the spacetime supersymmetries for either orientation of the round S7. Here we show that more general supermembrane solutions may be obtained by replacing the round S7 by any seven-dimensional Einstein space M7. These have symmetry P3 × G, where G is the isometry group of M7. For example, G = SO(5) × SO(3) for the squashed S7. For one orientation of M7, they preserve N 16 spacetime supersymmetries where 1 ? N ? 8 is the number of Killing spinors on M7; for the opposite orientation they preserve no supersymmetries since then M7 has no Killing spinors. For example N = 1 for the left-squashed S7 owing to its G2 Weyl holonomy, whereas N = 0 for the right-squashed S7. All these solutions saturate the same Bogomol'nyi bound between the mass and charge. Similar replacements of SD-p-2 by Einstein spaces MD-p-2 yield new super p-brane solutions in other spacetime dimensions D ? 11. In particular, simultaneous dimensional reduction of the above D = 11 supermembranes on S1 leads to a new class of D = 10 elementary string solutions which also have fewer supersymmetries.
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