PUB - Publikationen an der Universität Bielefeld

We study relations between quaternionic Riemannian manifolds admitting different types of symmetries. We show that any hyperKahler manifold admitting hyperKahler potential and triholomorphic action of S-1 can be constructed from another hyperKahler manifold (of lower dimension) with an action of S-1 that fixes one complex structure and rotates the other two and vice versa. We also study the corresponding quaternionic Kahler manifolds equipped with a quaternionic Kahler action of the circle. In particular we show that any positive quaternionic Kahler manifolds with S-1-symmetry admits a Kahler metric on an open everywhere dense subset. (C) 2007 Elsevier B.V. All rights reserved.