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S p ( 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 S p ( n ) U ( 1 ) ⊂ U ( 2 n ) × U ( 1 ) , then the manifold is locally isomorphic to the twistor space of a quaternionic Kähler manifo...

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Bibliographic Details
Published in:Journal of geometry and physics 2006-12, Vol.57 (1), p.323-337
Main Author: Alexandrov, Bogdan
Format: Article
Language:English
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Summary: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 S p ( n ) U ( 1 ) ⊂ U ( 2 n ) × U ( 1 ) , then the manifold is locally isomorphic to the twistor space of a quaternionic Kähler manifold with positive scalar curvature. If the manifold is complete, then it is globally isomorphic to such a twistor space.
ISSN:0393-0440
1879-1662
DOI:10.1016/j.geomphys.2006.03.005