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 Sfb 288 Differential Geometry and Quantum Physics

Abstract for Sfb Preprint No. 602

Sp(n)U(1)-connections with parallel totally skew-symmetric torsion.

B. Alexandrov

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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Copyright © 1999 Sfb 288, Mathematics 8-5, Strasse des 17 Juni 136, TU-Berlin, 10623 Berlin
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