On the quadric CMC spacelike hypersurfaces in Lorentzian space forms
Volume 145 / 2016
Colloquium Mathematicum 145 (2016), 89-98 MSC: Primary 53C42; Secondary 53B30, 53C50, 53Z05, 83C99. DOI: 10.4064/cm6442-10-2015 Published online: 22 April 2016
We deal with complete spacelike hypersurfaces immersed with constant mean curvature in a Lorentzian space form. Under the assumption that the support functions with respect to a fixed nonzero vector are linearly related, we prove that such a hypersurface must be either totally umbilical or isometric to a hyperbolic cylinder of the ambient space.