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We review coupled ${\rm SU}(3)$-structures, also known in the literature as restricted half-flat structures, in relation to supersymmetry.
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Madsen, T.B., Salamon, S.: Half-flat structures on S 3 × S 3 S^{3}\times S^{3} . Ann. Global Anal. Geom. 44, 369–390 (2013)
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Raffero, A.: Half-flat structures inducing Einstein metrics on homogeneous spaces. Ann. Glob. Anal. Geom. (2015). doi:10.1007/s10455-015-9457-1
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