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.   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 "bipolarized" those Lorentz manifolds having a "trivial" compactification. Here we show a geometric rigidity of non-bipolarized Lorentz manifolds; that is, they are (at least locally) warped products of constant curvature Lorentz manifolds by Riemannian manifolds.

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