We find metrics admitting supercovariantly constant spinor fields in a sequence of supersymmetric theories of increasing complexity. With a dilaton with varying coupling, or with axion and dilaton in an -invariant theory we find all such metrics; in SU(4) supergravity with axion and dilaton, we find all such metrics subject to an extra restriction.
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K. P. Tod (1995) studied this question.
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