Isometry Groups and Geodesic Foliations of Lorentz Manifolds. Part II: Geometry of Analytic Lorentz Manifolds with Large Isometry Groups

This is Part II of a series on noncompact isometry groups of Lorentz manifolds. We have introduced in Part I, a compactification of these isometry groups, and called "bi-polarized" those Lorentz manifolds having a "trivial " compactification. Here we show a geometric rigidity of non-bi-polarized Lorentz manifolds; that is, they are (at least locally) warped products of constant curvature Lorentz manifolds by Riemannian manifolds. 1 Introduction We continue here our investigation of noncompact isometry groups of compact Lorentz manifolds, started in Part I [21] which contains dynamical ingredients. Its fundamental tool was the notion of approximate stability. This second part (which is in fact fairly independent of Part I) is geometrical, and has the warped product construction as a fundamental tool. Recall that this is a construction in the class of pseudo-Riemannian manifolds, defined as follows. Let (L; h) and (N; g) be two pseudo-Riemannian manifolds, and w : L ! R + a (warping) ..