HyperKähler and quaternionic Kähler manifolds with S– symmetries
نویسنده
چکیده
We study relations between quaternionic Riemannian manifolds admitting different types of symmetries. We show that any hyperKähler manifold admitting hyperKähler potential and triholomorphic action of S1 can be constructed from another hyperKähler manifold (of lower dimention) with an action of S1 which fixes one complex structure and rotates the other two and vice versa. On the other hand, the above two types of manifolds are also related to positive quaternionic Kähler manifolds with S1–symmetry. We also show that any positive quaternionic Kähler manifolds with S1–symmetry admits a Kähler metric on an open everywhere dense subset.
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