Parallel spinors and connections with skew-symmetric torsion in string theory

We describe all almost contact metric, almost hermitian and G2-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 Vparallel spinors. In particular, we obtain partial solutions of the type // string equations in dimension n = 5, 6 and 7.