HyperKahler and quaternionic Kahler manifolds with S^1-symmetries

Andriy Haydys

doi:10.1016/j.geomphys.2007.11.004

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arXiv · 0706.4473

HyperKahler and quaternionic Kahler manifolds with S^1-symmetries

Andriy Haydys

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Abstract

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 dimention) with an action of S^1 which fixes one complex structure and rotates the other two and vice versa. We also study corresponding quaternionic Kahler manifolds equipped with a quaternionic Kahler action of the circle. In particular we show that any positive quaternionic Kahler manifold with S^1 symmetry admits a Kahler metric on an open everywhere dense subset.

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BibTeX RIS

Andriy Haydys. 2007-09-13. HyperKahler and quaternionic Kahler manifolds with S^1-symmetries. https://doi.org/10.1016/j.geomphys.2007.11.004

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