Isometry groups and geodesic foliations of Lorentz manifolds. II: Geometry of analytic Lorentz manifolds with large isometry groups. (English) Zbl 0946.53036

Zeghib, A.

Geom. Funct. Anal. 9, No. 4, 823-854 (1999).

Author’s abstract: “This is part II of a series on non-compact isometry groups of Lorentz manifolds. We have introduced, in Part I [ibid., 775-822 (see the review above)], 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”.

Reviewer: A.P.Stone (Albuquerque)

MSC:

53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C12	Foliations (differential geometric aspects)

Keywords:

bipolarized Lorentz manifold; compactification

Citations:

Zbl 0946.53034