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

Bogdan Alexandrov
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Abstract

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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Bogdan Alexandrov. 2004-07-08. Sp(n)U(1)-connections with parallel totally skew-symmetric torsion. https://arxiv.org/abs/math/0311248

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