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HyperKähler Potentials in Cohomogeneity Two

Piotr Kobak·Andrew Swann
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Abstract

A hyperKähler potential is a function rho that is a Kähler potential for each complex structure compatible with the hyperKähler structure. Nilpotent orbits in a complex simple Lie algebra are known to carry hyperKähler metrics admitting such potentials. In this paper, we explicitly calculate the hyperKähler potential when the orbit is of cohomogeneity two. In some cases, we find that this structure lies in a one-parameter family of hyperKähler metrics with Kähler potentials, generalising the Eguchi-Hanson metrics in dimension four.

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Piotr Kobak, Andrew Swann. 2000-01-05. HyperKähler Potentials in Cohomogeneity Two. https://arxiv.org/abs/math/0001024

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