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

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

2003-11-14

arxiv.org/abs/math/0311248v2

Mathematics

Differential Geometry

24 pages; some inessential changes

Scientific paper

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), considered as a subgroup of U(2n) x U(1), then the manifold is locally isomorphic to the twistor space of a quaternionic Kaehler manifold with positive scalar curvature. If the manifold is complete, then it is globally isomorphic to such a twistor space.

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