Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 492

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

Thomas Friedrich and Stefan Ivanov

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 $ abla$-parallel spinors. In particular, we obtain solutions of the type $II$ string equations in dimension $n=5,6$ and $7$.

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