Title: SU(3)-holonomy metrics from nilpotent Lie groups

2013.10.21 |

Date | Fri 28 Oct |

Time | 13:00 — 14:00 |

Location | Aud. G1 |

**Abstract:**

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).