Isospectrality of flat Lorentz 3-manifolds. (English) Zbl 1036.53048

Drumm, Todd A.; Goldman, William M.

J. Differ. Geom. 58, No. 3, 457-465 (2001).

Using methods of G. A. Margulis [Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 134, 190–205 (1984; Zbl 0547.57030)], the authors prove that the isometry of a hyperbolic flat Lorentzian 3-manifold is uniquely determined by its marked geodesic length spectrum. A similar result is obtained for flat Lorentzian 3-manifolds with free fundamental group. The first result has been generalised to arbitrary dimensions by Inkang Kim (unpublished when the review was written).

Reviewer: Sebastian Goette (Regensburg)

MSC:

53C50	Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics
53C22	Geodesics in global differential geometry

Keywords:

Lorentzian geometry; marked geodesic length spectrum; flat Lorentz manifolds

Citations:

Zbl 0547.57030