|Sfb 288 Differential Geometry and Quantum Physics|
Abstract for Sfb Preprint No. 602
Sp(n)U(1)-connections with parallel totally skew-symmetric torsion.
We consider the unique Hermitian connection with totally skew-symmetric torsion on a Hermitian manifold. We prove that if the torsion is parallel and the holonomy is $Sp(n) U(1) \subset U(2n) \times U(1)$, then the manifold is locally isomorphic to the twistor space of a quaternionic K\"ahler manifold with positive scalar curvature. If the manifold is complete, then it is globally isomorphic to such atwistor space.
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