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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 dimension) with an action of S1 that fixes one complex structure and rotates the other two and vice versa. We also study the corresponding...
It is known that nilpotent orbits in a complex simple Lie algebra admit hyperKähler metrics with a single function that is a global potential for each of the Kähler structures (a hyperKähler potential). In an earlier paper, the authors showed that nilpotent orbits in classical Lie algebras can be constructed as finite-dimensional hyperKähler quotient of a flat vector space. This paper uses that quotient...
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