Abstract.
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.
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Submitted: April 1998, final version: November 1998.
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Zeghib, A. Isometry Groups and Geodesic Foliations of Lorentz Manifolds. Part II: Geometry of Analytic Lorentz Manifolds with Large Isometry Groups. GAFA, Geom. funct. anal. 9, 823–854 (1999). https://doi.org/10.1007/s000390050103
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DOI: https://doi.org/10.1007/s000390050103