Characterization of Hyperbolic Cylinders in a Lorentzian Space Form

摘要

We give a characterization of the n -dimensional ( n ≥ 3) hyperbolic cylinders in a Lorentzian space form. We show that the hyperbolic cylinders are the only complete space-like hypersurfaces in an ( n + 1)-dimensional Lorentzian space form M ₁ ^{n +1}( c ) with non-zero constant mean curvature H whose two distinct principal curvatures l and m satisfy inf ( l - m )² > 0 for c ≤ 0 or inf ( l - m )² > 0, H ² ≥ c , for c > 0, where l is of multiplicity n - 1 and m of multiplicity 1 and l < m .