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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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Published in: | Journal of geometry and physics 2006-12, Vol.57 (1), p.323-337 |
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Main Author: | |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
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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. |
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ISSN: | 0393-0440 1879-1662 |
DOI: | 10.1016/j.geomphys.2006.03.005 |