Cohomogeneity-Three HyperKähler Metrics on Nilpotent Orbits
Identifieur interne : 000C90 ( Main/Exploration ); précédent : 000C89; suivant : 000C91Cohomogeneity-Three HyperKähler Metrics on Nilpotent Orbits
Auteurs : Martin Villumsen [Danemark]Source :
- Annals of Global Analysis and Geometry [ 0232-704X ] ; 2005-09-01.
English descriptors
Abstract
Abstract: Let $${\cal O}$$ be a nilpotent orbit in ℊℂ where G is a compact, simple group and ℊ = Lie(G). It is known that $${\cal O}$$ 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 $${\cal O}$$ 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 Sp3, su6, So7, So12 or e7 and otherwise is the unique G-invariant hyperKähler metric with G-invariant Kähler potential.
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DOI: 10.1007/s10455-005-6636-5
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