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

[摘要] 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(l) subset of U(2n) x U(1), then the manifold is locally isomorphic to the twistor space of a quaternionic Kahler manifold with positive scalar curvature. If the manifold is complete, then it is globally isomorphic to such a twistor space. (c) 2006 Elsevier B.V. All rights reserved.

[发布日期] 2006-12-31

[关键词] Hermitian manifold;nearly Kahler manifold;quaternionic Kahler manifold;twistor space;connection with totally skew-symmetric torsion;holonomy group