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SU(3)-holonomy metrics from nilpotent Lie groups

Diego Conti
Fredag, 28 oktober, 2011, at 13:00-14:00, in Aud. G1 (1532-116)
One way to construct explicit cohomogeneity one metrics with holonomy SU(3) is by means of an evolution flow in the sense of Hitchin. This amounts to fixing a hypo structure on the principal orbit G/H and solving a certain ODE, thus obtaining a metric with holonomy contained in SU(3) on the product of G/H with an interval. One can then try to extend to a complete metric by adding a special orbit of lower dimension. In this talk I will illustrate the classification of metrics of this type for which G is nilpotent of dimension five and H discrete. This classification requires in particular the solution of several ODE's. In order to reduce the number of parameters, one introduces a flow on the variety of nilpotent Lie algebras, obtained by interpreting the original flow in terms of gauge transformations and using the fact that the principal stabilizer H is discrete. Having classified the local metrics, one finds that none of them can be extended to a complete metric (except the flat metric).
Organiseret af: QGM
Kontaktperson: Jørgen Ellegaard Andersen