Parallel spinors and connections with skew-symmetric torsion in string theory.
We describe all almost contact metric, almost Hermitian and \(G_2\)-structures admitting a connection with totally skew-symmetric torsion tensor, and prove that there exists at most one such connection. We investigate its torsion form, its Ricci tensor, the Dirac operator and the \(\nabla\)-parallel spinors. In particular, we obtain partial solutions of the type II string equations in dimensions \(n = 5\), 6 and 7.
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