arXiv math/04060092004-06-01math.DG

Cohomogeneity-Three HyperKähler Metrics on Nilpotent Orbits

Martin Villumsen

英文摘要：

Let O be a nilpotent orbit in g^C where G is a compact, simple group and g=Lie(G). It is known that O carries a unique G-invariant hyperKähler metric admitting a hyperKähler potential compatible with the Kirillov-Kostant-Souriau symplectic form. In this work, the hyperKähler potential is explicitly calculated when O is of cohomogeneity three under the action of G. It is found that such a structure lies on a one-parameter family of hyperKähler metrics with G-invariant Kähler potentials if and only if g is sp(3), su(6), so(7), so(12) or e_7 and otherwise is the unique G-invariant hyperKähler metric with G-invariant Kähler potential.

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