报告地址：行健楼665
邀请人：陈慧斌 博士
摘要: The geodesic orbit property has been studied intensively for Riemannian manifolds. Geodesic orbit spaces are homogeneous and allow simplifications of many structural questions using the Lie algebra of the isometry group. Weakly symmetric Riemannian manifolds are geodesic orbit spaces. Here we define “naturally reductive” for pseudo–Riemannian manifolds and note that they are geodesic orbit spaces. In the Riemannian case the nilpotent isometry group for a geodesic orbit nilmanifold is abelian or 2–step nilpotent. Here we concentrate on the geodesic orbit property for Lorentz nil- manifolds G/H with G = N \rtimes H and N nilpotent. When the metric is nondegenerate on [n, n], we prove that N either is at most 2–step nilpotent as in the Riemannian situation, or is 4–step nilpotent, but cannot be 3–step nilpotent. When the metric is degenerate on [n,n], it shows that N is at most 2–step nilpotent. Both theorems give additional structural information and specialize to naturally reductive and to weakly symmetric Lorentz nilmanifolds. This is a joint work with Zhiqi Chen and J. A. Wolf.