Sp(n)U(1)-connections with parallel totally skew-symmetric torsion
Differential Geometry
2007-05-23 v2
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.
Keywords
Cite
@article{arxiv.math/0311248,
title = {Sp(n)U(1)-connections with parallel totally skew-symmetric torsion},
author = {Bogdan Alexandrov},
journal= {arXiv preprint arXiv:math/0311248},
year = {2007}
}
Comments
24 pages; some inessential changes